The conversation, after which Trump said he had a "very good" relationship with the Taliban's co-founder, comes as that agreement to withdraw U.S. troops from Afghanistan and begin Afghan peace negotiations seems threatened by renewed violence and a dispute over releasing Taliban prisoners.
Trump spoke to Abdul Ghani Baradar, who serves as the group's chief negotiator and also goes by Mullah Baradar, according to the militant group's spokesperson, who said the call lasted 35 minutes.
Afterward, he told reporters that his "relationship" with Baradar is "very good ... we had a good, long conversation today, and, you know, they want to cease the violence. They'd like to cease violence also."
That's not true. On Monday, the group's spokesperson said attacks would resume on Afghan government forces but not U.S. forces, and Monday into Tuesday, there were 33 attacks in 16 provinces, killing six people and wounding 14, an Afghan Interior Ministry spokesperson told ABC News. Five Afghan policemen also were reportedly killed during an attack on a security checkpoint, according to Reuters.
Instead, the militant group seems focused on steering clear of the U.S. and pushing toward a full American withdrawal.
"If the United States honors the agreement concluded with us, then we will have positive future bilateral relations," Baradar told Trump, according to his spokesperson.
According to the Taliban, Trump told Baradar, "It is a pleasure to talk to you. You are a tough people and have a great country, and I understand that you are fighting for your homeland. We have been there for 19 years, and that is a very long time, and withdrawal of foreign forces from Afghanistan now is in the interest of everyone."
The White House has not provided a readout of the call.
The agreement signed Saturday in Doha, Qatar, where chief U.S. negotiator, Zalmay Khalilzad, spent a year and a half negotiating with Baradar and others, lays out a full U.S. withdrawal, if the Taliban meets certain commitments -- to engage in national peace negotiations with other Afghans and to prevent Afghanistan from being a safe haven to terror groups, specifically al Qaeda.
To kick that process off, the U.S. agreed to draw down its forces from approximately 13,000 to 8,600 and close its five major military bases within 135 days, while the Taliban agreed to meet an Afghan national delegation for negotiations on March 10. The militant group does not recognize the government of President Ashraf Ghani, decrying it as a U.S. puppet, but members of the government will join civil society, tribal leaders and women in a "personal" capacity to make up the Afghan national team.
But in the days since the agreement was signed by Baradar and Khalilzad, with Pompeo as a witness, there's growing concern those intra-Afghan negotiations won't happen.
In addition to the renewed violence against Afghan security forces, there is a discrepancy between the two agreements the administration signed over releasing Taliban prisoners.
The U.S.-Taliban agreement says the U.S. will facilitate the release of up to 5,000 Taliban prisoners held by the Afghan government and up to 1,000 from the "other side" held by the Taliban, all of whom "will be released" by March 10, when negotiations begin. But a separate joint statement signed by the U.S. and Afghan governments on Saturday says only Ghani's government will discuss the "feasibility of releasing significant numbers of prisoners on both sides," without committing to any number or time frame.
"We have not made a commitment to release them. It's a sovereign Afghan decision. We will discuss the question of prisoners as part of a peace deal, which has to be comprehensive," Ghani told CNN on Sunday, refusing to release any Taliban prisoners -- a key leverage point for the government and potential security risk -- until those negotiations begin.
But the Taliban spokesperson said Monday the militant group will not participate in the negotiations until prisoners are released, leaving talks up in the air.
"Do not allow anyone to take actions that violate the terms of the agreement, thus embroiling you even further in this prolonged war," Baradar told Trump in their call, according to his spokesperson -- urging him to pressure Ghani to release prisoners.
Trump seemed to agree, reportedly telling Baradar that Pompeo "shall soon talk with Ashraf Ghani in order to remove all hurdles facing the intra-Afghan negotiations."
Asked about Ghani's hesitation, Trump said Ghani "may be reluctant," then denounced the Afghan government for doing "very well with the United States for many years, far beyond military, if you look at all the money that we've spent."
The State Department did not respond to questions about whether Pompeo called Ghani, but he was dismissive of Ghani's statements on Monday: "It shouldn't surprise anyone that the habits of old days are hard to be break and this will be a bumpy road going forward," he told Fox News in an interview.
Khalilzad, the chief U.S. negotiator seen with Baradar during the Trump call in a photo released by the Taliban, had been conducting some shuttle diplomacy between the rival Afghan political factions to push them along in their roles in the peace process. Pompeo alluded to that, saying the U.S. was "determined to get there" and push the process forward.
Amid all the issues, some Republicans in Congress have grown vocal about their opposition to the agreement.
Rep. Liz Cheney, the third-highest-ranking House Republican and daughter of former Vice President Dick Cheney, said Tuesday that she read the classified annexes of the deal in a Capitol Hill secure facility and, "My concerns remain. ... The documents do not include in them the things that Secretary Pompeo said they would," including enforcement mechanisms and a Taliban commitment to break with al Qaeda.
"What we have seen with this agreement," she added, "now concerns me as much as the Iranian nuclear deal did, now that I have seen the documents, now that there seems to be still no verification mechanism by which we are gonna enforce any of the so-called Taliban promises."
ABC News's Ben Gittleson contributed to this report from the White House and Aleem Agha from Kabul, Afghanistan.