The one-year travel ban is expiring for five senior Taliban leaders who were exchanged for Army Sgt. Bowe Bergdahl last year, raising the possibility that they can move freely around the world as early as Monday.

Under the terms of the May 2014 exchange, the five detainees were sent to Qatar, where officials there agreed to track their activities and prevent them from traveling out of the country. In return, Bergdahl was released to the U.S. military after being held captive by the Taliban for nearly five years after he walked away from his post in Afghanistan.

U.S. officials and Qatar have discussed the possibility of extending the travel ban after it expires June 1. However, the White House has not publicly announced any new agreement with Qatar, which means the five could leave the nation by the end of the month.

"In Congress, we spent a lot of time debating whether the Qataris were going to adequately keep an eye on them in the course of the 12 months," said Rep. Adam Schiff of California, the top Democrat on the House Intelligence committee. "My point all along was that I'm more worried about month No. 13 than the first 12."

Schiff has been privy to the details of the still-secret memorandum of understanding the U.S. reached with Qatar that put the five under a 12-month watch following their release.

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"The Qataris did pretty good -- I wouldn't say perfect," he said about the year-long monitoring. "But the big question is what comes next."

At least one of the five allegedly contacted militants during the last year while in the tiny nation. The White House confirmed that one was put under enhanced surveillance, but did not disclose further details about that contact.

Arizona Sen. John McCain, Chairman of the Senate Armed Services Committee, said last week, “I know that at least one has hard communication with the Taliban.”

South Carolina Sen. Lindsey Graham has said that one or more of the detainees had some members of the Al Qaeda-affiliated Haqqani militant group travel to Qatar to meet with them earlier in the year. Graham suggested it was an indication the group was reaching out to communicate with the Taliban Five.

Four of the five former detainees remain on a United Nations blacklist, which freezes their assets and has them under a separate travel ban. The U.N., however, has acknowledged in a report last year that its travel ban has been violated.

"Regrettably, the monitoring team continues to receive a steady -- albeit officially unconfirmed -- flow of media reports indicating that some listed individuals have become increasingly adept at circumventing the sanctions measures, the travel ban in particular,” the U.N. Sanctions Committee said.

The State Department insists that U.S. officials work to mitigate the risk of former Gitmo detainees returning to the fight, threatening Americans or jeopardizing national security. U.S. officials have noted that in the past that the five Taliban leaders are middle-aged or older, were former officials in the Taliban government and probably wouldn’t be seen again on any sort of battlefield, although they could still be active members of the Taliban.

Members of Congress have repeatedly expressed concern about what will happen after the travel ban expires. They have asked the Obama administration to try to persuade Qatar to extend the monitoring.

"It's impossible for me to see how they don't rejoin the fight in short order," said Rep. Ed Royce, R-Calif., chairman of the House Foreign Affairs Committee.

Sen. Kelly Ayotte, R-N.H., wrote Defense Secretary Ash Carter in March, asking him to take any step necessary to make sure the five do not return to the battlefield in Afghanistan. And earlier this month, the 13 Republican members of the House Intelligence committee wrote President Obama asking him to urge Qatar to extend travel restrictions on the former detainees indefinitely.  

"If, as scheduled, Qatar permits these five former detainees to possess passports and travel to Afghanistan or Pakistan when the memorandum of understanding expires on June 1, they will be at liberty to play an even more direct role in attacks against the men and women of our military," they wrote.

Lawmakers from both parties were irate when the five detainees were swapped for Bergdahl, who recently was charged with desertion. They complained that the White House did not give Congress a 30-day notification of the transfer, a requirement by law. In response, the White House said it could not wait 30 days because Bergdahl’s life was endangered.

After the transfer, the House Armed Services Committee demanded the Pentagon release internal documents about the swap. The committee received hundreds, but lawmakers complain that they are heavily redacted. The committee inserted language in the fiscal 2016 defense policy bill that threatens to cut Pentagon spending by about $500 million if the Defense Department doesn't provide additional information about the exchange.  

Army Lt. Col. Joe Sowers, a spokesman for the Defense Department, said the Pentagon has provided the committee with more than 3,600 pages of documents and redactions have been minimal.

The Associated Press contributed to this report.