WASHINGTON — President Trump’s nomination of Rex Tillerson for secretary of state cleared a Senate hurdle Monday, setting the stage for an extended debate over the president’s order banning travel from specific Muslim-majority countries and U.S. policy toward Russia.

Senators voted 56-43 to put Tillerson’s bid to be the nation’s chief diplomat on track for confirmation later this week. Minority Leader Chuck Schumer, D-N.Y., pressed unsuccessfully for a delay in the vote until Tillerson answered for Trump’s travel ban order.

Secretary of State-designate Rex Tillerson is on track for confirmation this week after clearing a hurdle Monday. Associated Press/Steve Helber

Trump’s order bars individuals from seven Muslim-majority countries from entering the U.S. for 90 days. Trump has repeatedly said the move is aimed at protecting the nation against extremists looking to attack Americans and American interests. But recent domestic acts of deadly extremist violence have been carried out either by U.S. citizens or by individuals whose families weren’t from the nations singled out.

Maine’s Sen. Angus King announced Monday that he will support the nomination of Rex Tillerson as secretary of state. Both he and Republican Sen. Susan Collins of Maine voted to set move ahead with the confirmation vote Monday.

“I have arrived at the conclusion that Mr. Tillerson can and will effectively lead the State Department and serve as a critical moderating influence on and counterweight to the more impulsive forces within the current Administration,” King, an independent, said in a news release Monday. “I still harbor concerns regarding Mr. Tillerson’s past connections to Russia, as well as some activities that occurred at ExxonMobil during his tenure, but, on balance, those concerns are ultimately outweighed by the need to have a strong and serious leader at the helm of the State Department – someone who can offer the President forceful, but thoughtful and measured judgment on the critical issues we face.”

Although many Democrats – including Schumer – will oppose Tillerson, they’ll need at least several Republicans to join them to derail the nomination. That appeared unlikely, even after two of the Senate’s leading Republican voices on national security voiced concern over Trump’s desire for a better relationship with Moscow.

Sens. John McCain of Arizona and Lindsey Graham of South Carolina also criticized Trump’s travel ban order and his failure to consult with key federal agencies, including the departments of Justice and Homeland Security.

“We fear this executive order will become a self-inflicted wound in the fight against terrorism,” McCain and Graham said. That elicited an angry tweet from Trump, who called the two GOP senators “weak on immigration” and accused them of “looking to start World War III.”

Whether Trump intends to lift U.S. sanctions against Russia will likely be another major theme in the Senate debate over Tillerson’s nomination, which is restricted to no more than 30 hours after Monday’s vote. The president last week was noncommittal, telling reporters at a news conference: “We’ll see what happens. As far as the sanctions, very early to be talking about that.”

But Democrats have doubted Tillerson’s willingness to be tough with Russia. Sen. Ben Cardin of Maryland, the top Democrat on the Foreign Relations Committee, said his responses to questions about sanctions against Moscow sounded more like answers a corporate executive would give instead of a prospective secretary of state.

McCain, the chairman of the Armed Services Committee, and Sen. Rob Portman, a member of the Foreign Relations Committee, last week warned the White House about easing any punishments on Moscow and vowed to turn the sanctions into law.

U.S. intelligence officials have concluded that Moscow meddled in the 2016 election to help Trump become president.

Obama in late December ordered sanctions on Russian spy agencies, closed two Russian compounds and expelled 35 diplomats the U.S. said were really spies. The new penalties add to existing U.S. sanctions over Russia’s actions in Ukraine, which have damaged Russia’s economy but had only limited impact on Putin’s behavior.

In 2014, Russia annexed Crimea in Ukraine, drawing widespread condemnation in Europe and the United States and a raft of penalties.

Relations are also tense over Putin’s backing of Syrian President Bashar Assad and allegations of Russian meddling in the U.S. elections.

Sen. Joe Manchin, D-W.Va., said last week he would support Tillerson. Manchin, who faces re-election in 2018 in a state that backed Trump heavily in the presidential election, said the former Exxon Mobil CEO’s business career “will bring a unique perspective to the State Department.”

Joining Manchin in voting to move ahead on the nomination were two other senators facing re-election in 2018 – Democrat Heidi Heitkamp of North Dakota and Independent Angus King of Maine. Democrat Mark Warner of Virginia also voted with the Republicans to push the nomination forward.

Separately, two Senate panels postponed votes scheduled for late Monday on two other Trump nominations – Steve Mnuchin to be treasury secretary and Linda McMahon, the former wrestling entertainment executive, to lead the Small Business Administration – because the time conflicted with a Democratic protest of Trump’s immigration order in front of the Supreme Court.

The delays were temporary, with votes expected Tuesday.