The US negotiator on Afghanistan voiced optimism Monday that the Taliban and government would begin peace talks and said President Donald Trump could pull US troops ahead of schedule if all goes well.

The Afghan government has been speeding up the release of prisoners, a key condition for the Taliban, after a ceasefire for the Eid al-Fitr holiday followed by a continued lull in fighting. "There's been a lot of progress in the last few days," said Zalmay Khalilzad, the US envoy who negotiated a deal with the Taliban in which Washington plans to end its longest-ever war.

"A lot of people have been pessimistic that we could get to this place where we're discussing where and when inter-Afghan negotiations would begin and that there would be enough progress on the prisoners issue," he told reporters.

But he did not set a date and cautioned that "still more needs to be done" on freeing prisoners. Abdullah Abdullah, who heads the government council on the talks, said Saturday he was ready for talks "at any moment."

Under the agreement with the Taliban, the United States will pull troops out of Afghanistan by mid-2021 in exchange for the insurgents' commitments to keep out Al-Qaeda and other foreign extremists. US officials have said that the withdrawal is already ahead of schedule due to coronavirus concerns and The Wall Street Journal reported last week that the Pentagon had drafted plans for Trump to leave late this year -- coinciding with the US election.

Khalilzad said the withdrawal was "the prerogative of the president, and if he thinks that the conditions have been met, then we could do it faster, but the key thing is whether the conditions have been met." The United States invaded Afghanistan in 2001 and toppled the Taliban regime over its  welcome to Al-Qaeda, which carried out the September 11 attacks.

A recent expert report to the UN Security Council said that Al-Qaeda and the Taliban "remain close" and were in regular consultations over the negotiations with the United States. Khalilzad downplayed the report, saying it largely covered a period before the February 29 deal signed in Qatar. "There is progress, but we will continue to monitor those activities very closely," he said of Taliban ties with Al-Qaeda.