WASHINGTON — Under legal pressure, the Obama administration will begin telling some suspected terrorists if and why they are on a list of tens of thousands of people banned from flying to, from or within the United States.

The new policy allows an American traveler who has been denied boarding a commercial airliner to petition the U.S. Transportation Security Administration once to find out whether he or she is on the no-fly list and a second time for an unclassified explanation of why he or she is on the list. In some cases, the government will not be able to provide an explanation because of national security concerns.

The changes partially lift a veil of secrecy enshrouding a policy that has been a centerpiece of the government’s counterterrorism efforts since the September 2001 terror attacks. But the American Civil Liberties Union, which has been challenging the constitutionality of the no-fly list in an ongoing federal lawsuit, said the changes don’t go far enough in giving travelers the legal due process they are entitled to, including seeing the evidence held against them and the opportunity to challenge it.

The explanations provided to six travelers so far, which were mandated by a federal judge, have been inadequate, the ACLU said.

For instance, in a letter to New Jersey resident Amir Meshal, the government’s explanation for his inclusion on the list was based on information the FBI obtained from Meshal when he was detained in Africa in 2007, ACLU attorney Hina Shamsi said. The ACLU considers Meshal’s detention to be unlawful and said he suffered abuse.

“From the face of the letter, a neutral decision-maker would have no idea whatsoever that any of that occurred,” said Shamsi.

The Justice Department declined to comment on the specific constitutionality challenges because of the ongoing lawsuit.

Justice Department spokeswoman Nicole Navas said, “We are committed to a process that protects Americans from terrorist threats while respecting privacy and safeguarding civil liberties.”

Last fall, there were about 64,000 people on the no-fly list, according to the government. Typically, less than 5 percent of those on the list are Americans.

Previously, the government’s policy was never to confirm or deny that a person is on the list, citing national security concerns. In most instances, travelers assume they are on the list because they must go through additional screening at airports or can’t board their flights.