The discussions included the issue of Taliban prisoners whose release by the Afghan government the insurgents are demanding, Suhail Shaheen, the Taliban spokesman in Doha said on Twitter.
The Taliban want the prisoners freed before they join talks with government officials and other Afghans on a political settlement to decades of war.
The State Department did not immediately respond to a request for comment.
"Both sides talked about the inception of intra-Afghan negotiations" and they "emphasized that the release of the remaining prisoners are essential for commencement of intra-Afghan negotiations," Shaheen wrote.
The meeting between Pompeo and Baradar, the Taliban's Doha-based deputy leader, came as Afghan security forces ended a siege of a major prison in eastern Afghanistan by Islamic State militants in which hundreds of prisoners escaped.
It was not immediately known if the escapees included any of the prisoners whose release the Taliban is demanding.
The release of the Taliban prisoners has become a major hurdle to the convening of intra-Afghan peace talks, which were to have started by March 10.
A Feb. 29 US-Taliban agreement for a US troop withdrawal called for Kabul to free up to 5,000 Taliban prisoners in return for the release by the insurgents of up to 1,000 government detainees.
The Taliban has released around 1,000 detainees. The Afghan government, under US pressure, has freed around 4,600 Taliban prisoners named on a list compiled by the insurgents.
Afghan President Ashraf Ghani, however, is resisting freeing the remaining 400 named on the list, contending they were involved in serious crimes, including a massive 2017 bombing against the German embassy and other bloody attacks.
Instead, Ghani is expected to release 500 prisoners who are not on the list, and has called a traditional assembly of tribal elders from across the country - known as a loya jirga - to consult on whether to free those remaining on the list.The assembly is expected to be held later this month.