WASHINGTON – Secretary of State Mike Pompeo said Sunday that peace talks in Afghanistan are dead "for now" and defended President Donald Trump's controversial, and now aborted, decision to invite Taliban leaders to Camp David.

A Taliban official, meanwhile, warned that Trump's decision to halt negotiations would lead to more American deaths as the extremist Islamic group continues to fight for more territory.

Pompeo said the Taliban's attack last week – in which a car bomb killed one American serviceman and 11 others – prompted Trump's decision to pull the plug on months of painstaking negotiations that, until Saturday, seemed on track to produce a peace deal.

"The Taliban tried to gain negotiating advantage by conducting terror attacks inside of the country," Pompeo said on CNN's "State of the Union," one in a string of television interviews he did Sunday.

"It made no sense for the Taliban to be rewarded for that kind of bad behavior," Pompeo said.

Trump might be willing to resume negotiations, Pompeo said, if Taliban leaders start to deliver on their promises, which include reducing violence in Afghanistan and ending their relationship with al-Qaida terrorists. In talks with Trump's top negotiator, the Taliban have promised not to allow Afghanistan to become a safe haven for al-Qaida or other extremist groups, such as the Islamic State.

But skeptics have said the Taliban, itself a militant Islamic group that harbored Osama bin Laden before the 9/11 attacks, cannot be trusted.

"Camp David is where America’s leaders met to plan our response after al Qaeda, supported by the Taliban, killed 3000 Americans on 9/11," Rep. Liz Cheney, R-Wyo., tweeted on Sunday. "No member of the Taliban should set foot there. Ever. The Taliban still harbors al Qaeda."

Pompeo acknowledged that Camp David has "a long history, an important history," as he put it in an interview on NBC's "Meet the Press." But "it's also had an important role in complex peace negotiations, sometimes with some pretty bad actors," he said.

The secretary of state said the negotiations, led by U.S. special representative Zalmay Khalilzad, had made "real progress." Khalilzad announced a framework agreement with the Taliban last Monday. Under that deal, the U.S. would withdraw more than 5,400 of its 14,000 troops in Afghanistan over the next five months if the Taliban reduced its attacks and met other conditions.

"We are in the midst of an agreement that will reduce tyranny and open it up to Afghans to sit back and talk about a dignified and sustainable peace," Khalilzad tweeted after his ninth round of talks with the Taliban.

In an interview Sunday with Fox News, Pompeo said the administration has now recalled Khalilzad, who has been briefing the U.S.-backed Afghan government.

Pompeo initially seemed to defend the emerging deal, saying the U.S. had "delivered" on its mission in Afghanistan after 18 deadly years of conflict. But on Sunday, he said there was more work to do and the U.S. would not enter into any deal unless the Taliban proved it was acting in good faith.

Asked on Fox News if the talks are "dead," Pompeo said, "For the time being, they are."

The Taliban said Trump's decision – which stunned lawmakers and foreign policy experts– would lead to more violence.

"The Americans will suffer more than anyone else for canceling the talks," Taliban spokesman Zabihullah Mujahid said in a statement, according to Reuters.

Uncertainty now surrounds Trump's hopes to fulfill a campaign promise to end America's longest war and bring U.S. troops home from Afghanistan. And he now faces blowback across the political spectrum for his plans to meet secretly with the Taliban, which allowed al-Qaida to flourish inside the Afghanistan and plot the 9/11 attacks on the U.S.

Trump made the announcement in a string of Twitter posts late Saturday, saying he had canceled the secret negotiations with Taliban leaders and was suspending negotiations with them.

"If they cannot agree to a ceasefire during these very important peace talks, and would even kill 12 innocent people, then they probably don’t have the power to negotiate a meaningful agreement anyway," Trump said. "How many more decades are they willing to fight?"

Taliban leaders and Afghan President Ashraf Ghani were preparing to travel to the United States to discuss an agreement to end the conflict that began in 2001, according to the president.

Lawmakers and foreign policy aides, including Republicans, blasted Trump for planning to sit down the Taliban, less than a week before the anniversary of the terrorist attacks of Sept. 11, 2001.

"Never should leaders of a terrorist organization that hasn’t renounced 9/11 and continues in evil be allowed in our great country," tweeted Rep. Adam Kinzinger, R-Ill. "NEVER. Full stop."

In a statement after Trump's announcement, Ghani's office said rebels need to stop their attacks: "Real peace will come when Taliban agree to a ceasefire."

After 9/11, U.S.-led forces invaded Afghanistan, toppled the Taliban and tried to foster democracy in the war-torn country. But remnants of the extremist group have been fighting the government ever since, and the Taliban now control about half the country again.

More than 2,400 American soldiers have been killed in the war, according to the most recent figures from the Pentagon. About 22,000 coalition troops are in Afghanistan now, 14,000 of them Americans.

Trump's hope for a speedy withdrawal of U.S. forces has drawn opposition from within his own administration, including military leaders who want a more phased approach. Critics fear a premature withdrawal would encourage the Taliban to retake control of the country.