Pompeo and Esper met Ghani on the sidelines of an international security forum in Munich as officials said a "reduction in violence" agreement is on the table and could be announced as early as the weekend.
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.