Afghan security guards stand on a wall as hundreds of people gather outside the international airport in Kabul, Afghanistan, on Tuesday. Associated Press

The Taliban’s top political leader arrived Tuesday in Afghanistan, as the militants moved toward organizing a new government and insisted that all Afghans and foreigners inside the country would be safe.

The Biden administration tentatively accepted the assurances but said it is interested in deeds, not words. The U.S. military said it had established direct lines of communication with the Taliban on the ground, and that evacuations of American and other civilians were proceeding calmly and quickly after Monday’s chaotic airport scenes.

At times, it seemed as if much of the world, and the citizens of Afghanistan, were holding their collective breath, waiting to see if the apparent calm and outreach were just tactical maneuvers by militants with a long history of brutality and isolation as they consolidate their grip on power.

“Ultimately, it’s going to be up to the Taliban to show the rest of the world who they are and how they intend to proceed,” White House national security adviser Jake Sullivan told reporters. “The track record has not been good, but it’s premature to address that question at this point.”

Military officials said their focus for now was only on what Sullivan called “the task at hand” of getting as many Americans, third-country nationals and Afghans considered at risk out of Afghanistan.

All of the Afghan civilians who swarmed the airport Monday in desperation have been cleared, Army Maj. Gen. Hank Taylor, deputy director for regional operations of the Joint Staff, said in Washington, and the airport “remains secure” and “open for military flight operations, as well as limited commercial flight operations.”

Hundreds of people gather near a U.S. Air Force C-17 transport plane at a perimeter at the international airport in Kabul, Afghanistan, on Monday. Associated Press/Shekib Rahmani

While “we remain vigilant,” Taylor said, “we have had no hostile interactions, no attack and no threat by the Taliban.”

The Air Force said it has launched an investigation into the deaths of Afghan civilians who were part of the crush of hundreds who surrounded a C-17 transport aircraft as it tried to take off Monday, in scenes that President Biden later called “gut-wrenching.”

Amid the deteriorating security situation, the crew decided to depart even before it offloaded the plane’s cargo, as some of the Afghans tried to grab onto the aircraft’s wheels. What appeared to be at least one, and perhaps two, bodies were seen falling to the ground as the plane gained altitude, and human remains were later found in a wheel well when the plane later landed at Al Udeid air base in Qatar.

The probe will be carried out by the service’s Office of Special Investigations and is expected to include both interviews and an examination of viral videos of the departing flight. An Air Force statement said the review “will be thorough to ensure we obtain the facts regarding this tragic incident.”

“Our hearts go out to the families of the deceased,” the statement said.

After civilians were cleared from the airport, nine massive C-17 transport planes arrived overnight, Taylor said, delivering equipment and about 1,000 additional U.S. troops – bringing the total deployed at the airport to about 4,000. Seven planes took off, carrying what he said were “approximately 700 to 800 passengers,” 165 of them Americans.

Hundreds of people run alongside a U.S. Air Force C-17 transport plane as it moves down a runway of the international airport in Kabul, Afghanistan, on Monday. U.S. military officials said Tuesday that evacuations of American and other civilians were proceeding calmly and quickly, after Monday’s chaotic airport scenes.  Verified UGC via AP

Later Tuesday, a White House official told reporters that the number of military evacuation flights had jumped to 13, evacuating 1,100 U.S. citizens, permanent residents and their families. The total number of people evacuated had climbed to about 3,200, the official said, speaking on the condition of anonymity because of the sensitivity of the issue.

Assuming operations expand as quickly as intended, Taylor said, “we predict that our best effort could look like 5,000 to 9,000 passengers departing per day,” on at least two dozen flights. U.S. military air traffic controllers have also directed the arrival and departure of planes from other countries arriving to pick up their officials and citizens.

Taylor said at least another 2,000 U.S. troops were expected to join the 4,000 on the ground at the joint military-civilian airport complex. Although Biden could extend his deadline of Aug. 31 to complete the evacuation of what may be as many as 100,000 people, he has not yet done so.

The State Department said all U.S. diplomats who are leaving have been evacuated. Overnight, a message went out from the U.S. Embassy, currently operating at the airport, to a list of Americans and others in Kabul approved for departure telling them how and when to make their way to the airport. The department has sent veteran diplomat John Bass to Kabul to oversee the logistics of that part of the operation.

U.S. troops are restricted to the airport, and administration officials were peppered throughout the day with questions about Americans, Afghans and others – many of whom had received notice from the embassy to show up – who were turned back at Taliban checkpoints along the way to the airport.

Asked if the United States, in its talks with the militants, would provide transportation or otherwise ensure their arrival, the State Department’s Price said, “I can’t speak to individual cases.

“What I can speak to is what we are seeking to do. We are doing everything in our power to effect a corridor for safe passage” for Americans living in Afghanistan who want to leave, as well as other civilians, including Afghans who worked for the American effort there and qualify for a special U.S. visa program or who may be at risk for other reasons.

The Taliban has “informed us that they are prepared to provide the safe passage of civilians to the airport and we intend to hold them to that commitment,” national security adviser Sullivan said.

But those assurances apparently apply only to evacuees in Kabul. Administration officials told a bipartisan group of Senate staffers Tuesday that there are an estimated 10,000 to 15,000 U.S. citizens still in Afghanistan, according to two Senate aides, with no current plan to evacuate those who are still outside the capital.

Arrangements with the Taliban over the airport were first discussed Monday in Doha, Qatar, by Marine Gen. Kenneth “Frank” McKenzie, head of the U.S. Central Command, and Abdul Ghani Baradar, the Taliban co-founder, political director and de facto leader. Pentagon spokesman John F. Kirby said those discussions were now taking place between U.S. commanders and Taliban officials in Kabul.

Baradar was also in close communication with Zalmay Khalilzad, the U.S. envoy to now aborted peace negotiations with the Afghan government of President Ashraf Ghani, who fled Afghanistan as the Taliban entered Kabul on Sunday. Baradar’s departure Tuesday morning from Doha to Kandahar, Afghanistan’s second-largest city, effectively moved the center of diplomatic gravity to Afghanistan itself.

Baradar’s homecoming suggested the Taliban was nearing an announcement on the official formation of a new government. Taliban leaders, including Baradar, have been in talks with an ad hoc “coordinating committee” led by former Afghan President Hamid Karzai and Abdullah Abdullah, who was Ghani’s chief negotiator in the unsuccessful Doha negotiations.

The Taliban has not yet declared a governing structure or named any officials, and observers said the expectation was that there would be a formal handover, perhaps by the Karzai committee.

At an unprecedented news conference in Kabul, longtime Taliban spokesperson Zabiullah Mujahid said that “nobody will be harmed in Afghanistan,” including anyone who had participated in the military or the previous government, women and foreigners.

While reluctant to crack the apparent fragile calm that is allowing the evacuations to proceed, the Biden administration expressed skepticism but a wait-and-see attitude, to the apparent ire of many lawmakers. Republicans, in particular, continued to sharply criticize Biden for “losing Afghanistan.”

But the Democratic chairmen of the House Foreign Affairs and Senate Foreign Relations Committees both pledged to hold public hearings to grill the administration about Biden’s decision last spring to withdraw all U.S. troops, the ensuing Taliban victory and chaotic evacuations.

Many warned not to trust the militants and said global terrorists – primarily al-Qaida – would once again find a haven in Afghanistan where they can expand and plot new attacks against the United States.

Both the Pentagon and the State Department repeated administration assurances that U.S. counterterrorism capabilities remained strong, despite the absence of a presence in Afghanistan.

Price, the State Department spokesperson, said that “any future relations between the Taliban and the United States … is going to be predicated on deeds.” Over the weekend, the Treasury Department ordered the freezing of billions of dollars in Afghan government reserves held in U.S. bank accounts, blocking Taliban access to the funds.

“If the Taliban says that they are going to respect the rights of their citizens, we will be looking for them … to make good on that statement. Just as importantly,” Price said, “the world is going to be looking for them to make good on that statement.”

The rest of the world varied in its reaction. Canadian Prime Minister Justin Trudeau said Canada had “no plans” to recognize the Taliban but echoed the U.S. “wait-and-see” posture.

China and Russia have both indicated they might be willing to establish diplomatic ties with the new government when it emerges.

In Brussels, European Union foreign policy chief Josep Borrell stopped short of calling for recognition but indicated there will have to be a dialogue “to prevent a humanitarian and potential migratory disaster.”

“We have to get in touch with authorities in Kabul,” Borrell said, “whatever they are. The Taliban have won the war.”