Mullah Abdul Ghani Baradar, the leader of the Taliban delegation, and Zalmay Khalilzad, US envoy for peace in Afghanistan, shake hands after signing an agreement at a ceremony between members of Afghanistan's Taliban and the US in Doha, Qatar February 29, 2020.
However, it was not known whether there was any mention during the call of allegations that some Taliban militants received money to kill US and North Atlantic Treaty Organisation soldiers in Afghanistan.
The Taliban on Tuesday reaffirmed their commitment to the landmark deal signed between them and the United States in February in a video call with Secretary of State Mike Pompeo.
The New York Times reported last week that US intelligence officials concluded months ago that Russian military intelligence offered bounties to Taliban-linked militants to kill USA troops.
Trump has denied being informed of the assessment and the White House said Monday that the information had been kept from him because the intelligence underpinning it was unverified, marking an unusual move since it is rare for intelligence to be proven without any doubt before presenting it to senior government officials.
That month, the USA had pledged to withdraw all its troops from Afghanistan by mid-2021 in return for security guarantees from the Taliban in a bid to pave the way for negotiations between Afghanistan's warring sides.
Trump has insisted that he was not briefed but lawmakers of the rival Democratic Party and even some Republicans have demanded further explanations.
The call comes as the US peace envoy, Zalmay Khalilzad, is touring the region in efforts to advance the deal.
He was in Uzbekistan on Tuesday and was expected in the Pakistani capital Islamabad later in the day or on Wednesday; he is expected to travel to Qatar where the Taliban maintain a political office.
The US Embassy in Kabul did not immediately issue a statement.
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.
Baradar told Pompeo that "according to the agreement, we do not allow anyone to use Afghan soil against the USA and other countries", Taliban spokesman Suhail Shaheen said in a statement on Twitter on Monday.
The talks are expected to begin some time in July - if both sides abide by a promise laid out in the U.S. -Taliban deal to release thousands of prisoners.
Kabul and some foreign countries have raised concerns about the release of about 200 prisoners they say are involved in major attacks in Afghanistan.
Baradar complained about new Afghan military checkpoints in areas under Taliban control while Pompeo said Washington wanted to see a reduction in violence, according to the tweet.
Violence in Afghanistan has continued to spike since a three-day ceasefire in May for Eid al-Fitr. On Monday, 23 civilians were killed in an attack on a busy market in the southern province of Helmand, a Taliban heartland.
The Afghan government said a powerful bomb and mortar fire by the Taliban caused the deaths.