MUNICH (AP) — A senior U.S.official said Friday the United States and the Taliban have reached a truce agreement that will take effect “very soon” and could lead to withdrawals of American troops from Afghanistan.

The official said the agreement for a seven-day “reduction in violence” to be followed by the start of all-Afghan peace talks within 10 days is “very specific” and covers the entire country including Afghan forces.

The developments come as U.S. Secretary of State Mike Pompeo and Defense Secretary Mark Esper met Friday in Munich with Afghanistan's President Ashraf Ghani. They spoke on the sidelines of an international security forum in Munich.

A truce had been widely anticipated, and President Donald Trump has agreed in principle to the deal, which could lead to the start of significant U.S. troop withdrawals from Afghanistan, according to U.S. officials.

The final details were hammered out in recent days by U.S. special envoy for Afghanistan Zalmay Khalilzad and Taliban representatives in Doha, Qatar. Khalilzad was in Munich and attended Pompeo and Esper's meeting as did Gen. Scott Miller, the commander of the U.S.-led international force in Afghanistan.

People familiar with the plan's outlines say it calls for the successful conclusion of the weeklong truce to be followed within 10 days by the start of all-Afghan negotiations to set the road map for the country's political future.

U.S. officials have brushed aside claims that a Taliban ultimatum forced their hand. And they noted that, despite Trump’s campaign pledge to withdraw American troops from Afghanistan and elsewhere, the Republican president has nixed previous deals that appeared close in response to attacks on U.S. forces.

The Trump administration will have to convince U.S. lawmakers who have been skeptical of the peace process. One of them, Sen. Lindsey Graham, S-S.C., said he was not yet ready to support fewer than 8,600 troops in Afghanistan.

“I find it difficult to believe that the Taliban renounce al-Qaida in a serious way, but I want to give it a chance,” he said on the sidelines of the Munich Security Conference. “If you go below 8600, and you’re putting our homeland at risk, unless there’s a fundamental change on the ground.”

Asked what triggered his evolution in thought, Graham said, “After 18 years, let’s give it a whirl. Let’s give it a chance. If the Taliban seems willing to talk to the Afghan government, let’s see what happens.”

Joe Gould of Defense News contributed to this report.