President Donald Trump said Thursday that the United States is "very close" to a peace deal with the Taliban guerrillas in Afghanistan.

"I think we're very close. I think there's a good chance that we'll have a deal and we'll see," he told Geraldo Rivera's "Roadkill" radio show.

"That doesn't mean we'll have one but we'll know over the next two weeks," he said.

Trump spoke amid growing signs of agreement on a week-long "reduction of violence."

US Secretary of State Mike Pompeo said on the way to the Munich Security Conference, where he is expected to meet Afghan President Ashraf Ghani, that talks had "made real progress over the past couple of days."

US Defense Secretary Mark Esper said after a NATO meeting in Brussels that the two sides have "negotiated a proposal for a seven-day reduction in violence."

Trump was not clear if he was talking about the proposed limited pause in hostilities or something broader.

"We're having very good dialogue, we'll see and we'll know over the next week or two," he said. The Taliban, "they'd like to make a deal, too." 

The announcement came a day after Afghan President Ashraf Ghani reported "notable progress" in negotiations with the Islamist insurgents.

Shortly before Trump statement, Defense Secretary Mark Esper said, "The United States and the Taliban have negotiated a proposal for a seven-day reduction in violence." 

"We've said all along that the best, if not the only, solution in Afghanistan is a political agreement. Progress has been made on that front and we'll have more to report on that soon, I hope," he said after a NATO meeting in Brussels.

Esper did not say when the partial truce would begin, but on Wednesday a Taliban official told AFP that the group would begin a "reduction of violence" on Friday.

"It is our view that seven days for now is sufficient but in all things our approach to this process will be conditions based, I will say it again, conditions based," Esper said.

"So it will be a continual evaluative process as we move forward, if we go forward."

US Secretary of State Mike Pompeo, speaking to reporters onboard a plane to the Munich Security Conference where he is expected to meet Ghani, said talks had "made real progress over the past couple of days." 

"We hope we can get to a place where we can get a significant reduction in violence not only on a piece of paper but demonstrated, the capability to actually deliver a serious reduction in violence in Afghanistan," he said.

"If we can get there, if we can hold that posture for a while, then we'll be able to begin the real, serious discussion, which is all the Afghans sitting at a table, finding a true reconciliation, a path forward."

Washington and the insurgents have been locked in gruelling talks that have stretched over more than a year, seeking an end to what has already become America's longest war.

'Long overdue'

Citing Afghan and US officials, the New York Times has reported that President Donald Trump had given conditional approval to a deal with the Taliban to allow him to start withdrawing US troops.

"It will be a difficult set of conversations, one that's long overdue," Pompeo said. "It would also give us the opportunity to reduce the footprint not only for America’s forces there but for all forces."

The United States currently has between 12,000 and 13,000 troops in Afghanistan, more than 18 after it invaded to overthrow the then Taliban government in the wake of the September 11 attacks. 

The only other time there has been a Taliban ceasefire since the regime's overthrow was in 2018, during the first three days of Eid at the end of the holy month of Ramadan.

It led to moving scenes such as Afghans sharing ice cream with Taliban fighters and snapping selfies. But afterwards, the violence resumed.

The number of clashes between the insurgents and US-backed government forces jumped to record levels in the last quarter of 2019, according to a recent US government watchdog report.