The United States also said it would not relent in fighting the militants as Trump cited a Taliban attack that killed a US soldier for scuttling the unprecedented meeting.
Trump said he had invited Taliban leaders, as well as Afghan President Ashraf Ghani, for talks Sunday at the presidential retreat of Camp David on a draft deal that would see the United States pull out thousands of troops and wind down its longest-ever war.
Secretary of State Mike Pompeo, in a series of television interviews Sunday, did not rule out a return to talks but said the United States needed a "significant commitment" from the Taliban.
"I'm not pessimistic," Pompeo told NBC. "I've watched the Taliban do things and say things they've not been permitted to do before."
"I hope it's the case the Taliban will change their behavior," he said on ABC.
"In the end, this will be resolved through a series of conversations," he added, urging the Taliban to drop its long-running refusal to negotiate with Ghani's internationally recognized government.
He said that Trump had not decided whether to go ahead with a withdrawal, which under the draft deal would pull 5,000 of the roughly 13,000 US troops from Afghanistan next year.
But he warned that the United States was also inflicting a toll on the Taliban, saying that US forces had killed more than 1,000 insurgents in the past 10 days alone.
"If the Taliban don't behave, if they don't deliver on the commitments they made to us for weeks and in some cases months, the president of the United States is not going to reduce the pressure," Pompeo said on CNN.
'Americans will be harmed'
Veteran US negotiator Zalmay Khalilzad had spent a year meeting with the Taliban, who confirmed that they considered the deal finished.
Taliban spokesman Zabihullah Mujahid said that Trump showed "neither experience nor patience."
"Americans will be harmed more than any other" by Trump's decision, a Taliban statement warned.
US "credibility will be harmed, their anti-peace stance will become more visible to the world, their casualties and financial losses will increase, and the US role in international political interaction will be discredited even further," it said.
But the spokesman said that the Taliban still believe "that the American side will come back to this position" of talks that seek "the complete end of the occupation."
The office of Ghani, whose government is rejected by the Taliban as illegitimate, cautiously saluted the "sincere efforts of its allies" after Trump called off the summit.
The Afghan presidency in a statement also "insisted that a real peace can only be achieved if the Taliban stop killing Afghans and accept a ceasefire, and face-to-face talks with the Afghan government."
Trump's dramatic about-face came weeks before Afghanistan holds presidential elections, raising fears that the Taliban will step up their campaign of violence to disrupt voting.
Criticism ahead of 9/11
Trump relishes dramatic gestures, such as meeting North Korean leader Kim Jong Un, but the idea of inviting Taliban leaders to US soil still stunned Washington.
The would-be talks angered even some allies of Trump, who noted that the Taliban would be visiting three days before the 18th anniversary of the September 11 attacks, which triggered the US invasion of Afghanistan.
"Camp David is where America's leaders met to plan our response after Al-Qaeda, supported by the Taliban, killed 3,000 Americans on 9/11. No member of the Taliban should set foot there. Ever," tweeted Liz Cheney, a Republican congresswoman and daughter of former vice president Dick Cheney.
Considering Trump's penchant for bombast, some questioned if the summit was even set to take place.
"I'm still looking for confirmation an actual, physical trip to Camp David was planned," Democratic presidential candidate Julian Castro told CNN, while adding: "It's very odd to invite a terrorist organization like that to Camp David."
Pompeo said that Trump had said of the Taliban, "I want to look them in the eyes, I want to see if we can get to the final outcome that we need so we could sign off on the deal."
On the eve of the canceled summit, Pompeo traveled to the Dover Air Force Base in Delaware for the return of the remains of the US soldier killed in Kabul, Elis Barreto Ortiz.
The United States also said it would not relent in fighting the militants as Trump cited a Taliban attack that killed a US soldier for scuttling the unprecedented meeting