Mr Pompeo was set to meet with Afghan President Ashraf Ghani along with his arch-rival Abdullah Abdullah, who also claims the presidency, following a contested election last year.
According to a pool report from a journalist accompanying Mr Pompeo, the top US diplomat was welcomed by special envoy Zalmay Khalilzad – the lead US negotiator in recent talks with the Taliban – after arriving at Kabul airport.
The visit comes just a day after the Afghan government and the Taliban held their first discussion on arranging prisoner exchanges – a key step in a broader push for peace following a withdrawal deal signed between Washington and the militants last month.
The agreement established a framework for bringing to an end America’s longest war following the invasion of Afghanistan in 2001.
Mr Khalilzad tweeted on Sunday that it was “urgent” to quickly conclude plans for the prisoner swap – as called for in the US pact with the Taliban – with the coronavirus pandemic complicating diplomatic contacts.
The deal called for the release of up to 5,000 Taliban fighters held by Kabul, and up to 1,000 members of the Afghan government forces in insurgent hands.
That was meant to take place before the start of peace talks originally set for March 10 between the government – which was not a party to the negotiations that produced the Doha deal – and the Taliban.
After initially refusing to release the Taliban prisoners, Mr Ghani announced that the authorities would free 1,500 insurgents as a “gesture of goodwill” with plans to free another 3,500 prisoners after the talks are underway.
The Taliban rejected the offer.
The Doha accord also calls for the gradual withdrawal of American and other foreign troops over a 14-month period – the main focus of the US diplomatic efforts.
The first phase of that withdrawal has already begun, though some troop movements have been slowed by the coronavirus pandemic.
In exchange, the Taliban committed cut ties with militant groups like Al Qaeda and promised to negotiate for the first time with Kabul.
But since the Doha agreement was signed, the Taliban have carried out scores of attacks.
Political chaos in Kabul has further complicated matters, with Mr Ghani’s former chief executive Mr Abdullah also claiming the presidency following last September’s bitterly disputed election.
The impasse and continued fighting along with the world’s preoccupation with coronavirus has sparked fears the window for a peace deal is closing fast.
Afghan health officials have reported just 40 cases of the novel coronavirus and one death to date.
However, health experts fear the contagion is spreading as tens of thousands of Afghans have returned home in recent weeks after fleeing virus-hit Iran.