Earlier, the Taliban said Baradar reaffirmed during the call the group's commitment to the peace process in Afghanistan and reiterated a pledge not to strike USA forces.
Pompeo and Mullah Abdul Ghani Baradar held a video conference late on Monday in which Pompeo pressed the armed group to reduce violence in Afghanistan and discussed ways of moving a peace deal signed between the USA and the Taliban in February forward, Taliban spokesman Suhail Shaheen tweeted.
Taliban has denied its fighters received any Russian bounties, and the group's Qatar-based chief negotiator Mullah Abdul Ghani Baradar reiterated their pledge not to strike against the US.
Increasing violence and a contentious prisoner swap between the Afghan government and the Taliban have delayed talks that were to have begun in March between the insurgent group and a team mandated by Kabul.
The comment comes amid an uproar over reported USA intelligence that Russia's military intelligence agency offered the Taliban payments to kill American troops in Afghanistan.
The call comes as U.S. President Donald Trumpfaces mounting pressure to explain his actions after being reportedly told that Russian spies a year ago had offered and paid cash to Taliban-linked militants for killing American soldiers.
Taliban spokesman Suhail Shaheen tweeted that Monday's talks between the official, Mullah Baradar, and Pompeo focused on full implementation of the Doha accord and the withdrawal of foreign troops, as well as the release of prisoners, intra-Afghan talks, and a reduction in fighting.
The New York Times on Monday said it had information that Trump had received a written briefing about the bounties in as early as February.
The Doha agreement, signed between the United States and Taliban in February, drew up plans for a withdrawal of foreign forces from the war-torn country in exchange for security guarantees from the insurgent group.
The call comes as the US peace envoy, Zalmay Khalilzad, is touring the region in efforts to advance the deal. Khalilzad will meet with Taliban leaders from their political office in Doha, Qatar later this week, and ahead of that, Pompeo spoke to them via video teleconference late Monday.
He will not be going to the Afghan capital, Kabul, due to the dangers presented by the coronavirus and instead will video conference with Afghan leaders.
Afghanistan's dilapidated healthcare system is grappling with the pandemic, with the number of infections thought to far outnumber the official tally of more than 31,000 cases, including 733 deaths.
The Taliban insist negotiations will begin only after Kabul completes the release of 5,000 of the group's militants held in Afghan jails as agreed in the deal with Washington.
Violence in Afghanistan has continued to spike since a three-day ceasefire in May for a major Muslim holiday.
The UN mission called on the Afghan government to set up an independent investigation and urged both the Taliban and government forces to stop fighting in civilian areas. As civilian casualties rise, both the Taliban and the government blame each other.
Pakistan players cleared after COVID tests
Pakistan are scheduled to play three Test matches and three Twenty20 internationals behind closed doors in August-September. The tourists will then move to Derbyshire's Incora County Ground on July 13 to begin internal warm-up matches.