Speaking to reporters traveling with him to the 2020 Munich Security Conference, Pompeo said Trump gave the green light to continue the talks, and that Washington was seeking to secure a significant reduction in violence before deeper discussions involving all Afghans can begin.
The prospect of a deal gives President Trump the opportunity to make good on his promise to remove USA troops from Afghanistan.
An agreement on a major troop withdrawal would be a boost for Trump, who has repeatedly promised to stop "endless wars", as he seeks re-election.
One of them: US negotiators will likely book the best to come to the support of all Afghan forces with air power.
AP reported that if violence subsided, it would lead to an agreement being signed between the United States and the Taliban, followed by, within 10 days, all-Afghan negotiations to establish a road map for the political future of a postwar Afghanistan.
The weeklong reduction in violence, officials say, will pave the way for comprehensive talks on a peace agreement that could finally end the almost two-decade-long war.
"I think we're very close", Trump said on a podcast broadcast on iHeart Radio when asked if a tentative deal had been reached.
"We've said that the best-if not only-solution in Afghanistan is a political agreement".
US President Donald Trump previously called off the peace talks because of an attack that killed two Americans.
"Well, the idea is to have a period that can initiate talks and then make progress on a real, sustainable, comprehensive peace deal", he said. The phase out of US troops will be happen in stages. "We have the basis for one on the table, we are taking a hard look at it, we are consulting with our allies, we are consulting with Congress and others".
-Taliban agreement would likely include calls for a permanent cease-fire, a drawdown of American forces in Afghanistan, and a framework for direct talks between the Taliban and the USA -backed government in Kabul, which the Taliban thus far has refused to recognize or engage with directly. The US officials and Afghan Taliban will be signing the deal in Qatar's Doha.
Originally, the Taliban agreed simply that it wouldn't attack important population centers, but USA negotiators pushed for a broader cessation of violence. Taliban insurgents have a strong presence in the region.