WASHINGTON (Reuters) - U.S. President Joe Biden sent the head of the CIA to meet the Taliban's leader on Monday in the highest level diplomatic encounter since the militant group took over the Afghan capital, U.S. media reports said on Tuesday.

       The Washington Post, citing U.S. officials who spoke on the condition of anonymity, said Central Intelligence Agency Director William Burns met Taliban leader Abdul Ghani Baradar in Kabul on Monday as the Biden administration evacuated U.S. citizens and other allies amid chaos at Kabul airport ahead of an Aug. 31 deadline.

       A CIA representatives said the agency had no comment. The White House did not respond to a request for comment.

       NBC News also reported that Burns and Baradar met, citing a senior diplomat in the region and another source familiar with the matter. Fox News also reported the meeting, citing one unnamed U.S. official.

       Biden last week said U.S. troops may stay in Afghanistan past the deadline next week in order to evacuate Americans.

       On Monday, two Taliban sources told Reuters it would not extend the deadline for Western forces to leave.

       (Reporting by Susan Heavey; Editing by Andrew Heavens and Angus MacSwan)