The Taliban says Americans have the most to lose from cancelling peace negotiations that sought to end the 18-year war in Afghanistan.
In a statement, the group claimed all was going well until the last moment.
US President Donald Trump fired off a series of tweets on Saturday night, calling off the secret meeting at his Camp David retreat the following day.
He said his decision came after the Taliban admitted to being behind a recent attack that killed a US soldier.
What had been planned?
In an unexpected move, Mr Trump had arranged to meet with senior Taliban leaders and Afghan President Ashraf Ghani at the Maryland retreat.
The meetings were likely to have been kept separate, as the Taliban refuses to talk directly with the Afghan government, insisting they are American puppets.
In 2001, US-led forces overthrew the Taliban government in Afghanistan because the militants had given safe haven to the al-Qaeda network to plan the attacks on the US on 11 September.
On Fox News on Sunday, US Secretary of State Mike Pompeo defended the intention to host the Taliban on US soil, days ahead of the attacks' anniversary.
He said Camp David was chosen because it has held difficult peace negotiations in the past. "It's almost always the case that you don't get to negotiate with good guys," he added.
How far had things come?
Nine rounds of talks had already taken place between the US and Taliban representatives in Doha, the capital of the Gulf state of Qatar.
On 3 September, the top US negotiator announced a peace deal "in principle".
As part of the proposed deal, the US would withdraw 5,400 troops within 20 weeks, in return for Taliban guarantees that Afghanistan would never again be used as a base for terrorism.
The US currently has about 14,000 troops in Afghanistan.
What else did the Afghan parties say?
In the statement, Taliban spokesperson Zabihullah Mujahid also accused the US of lacking maturity and experience, after pulling out of talks over one incident.
He also said that the Taliban and the Afghan government had agreed to talks on 23 September. The Afghan government has not confirmed this.
In a news conference in Kabul, a spokesperson for President Ghani simply repeated a long-standing wish for direct negotiation with the group.
"We strongly believe in a process that can be led and owned by Afghan government and Afghan people," said Sediq Sediqqi.
What sparked the cancellation?
On Thursday, a Kabul car bombing carried out by the Taliban killed 12 people, including a US soldier. A Romanian soldier serving with the Nato-led mission was also killed.
But the Taliban had never agreed to end their violent campaign against Afghan and foreign forces while the peace talks were taking place. Sixteen US troops have been killed this year.
A recent escalation of violence had deepened fears that a looming US-Taliban agreement would not end the daily fighting in Afghanistan and its toll on civilians.
Yet Kabul residents on Sunday questioned why the death of one US soldier should scupper prospects for peace.
"So, the Afghans who have been losing their sweet lives during all these years, is their blood worthless?" asked one grocery shop owner who spoke to the BBC's Pashto language service.
Ever since the US envoy Zalmay Khalilzad arrived in Kabul a week ago with news of "a deal in principle", there have been almost daily Taliban attacks, with a growing chorus of anger in Afghanistan - and the US.
The Taliban say they're targeting foreign forces. But time and again, Afghan civilians are suffering.
The new agreement is said to only include a commitment to reduce violence. A senior US diplomat explained they'd accepted the Taliban argument that a ceasefire was their main bargaining chip for Afghan talks set to follow the US negotiations.
A senior Afghan official angrily told me "a ceasefire is our bargaining chip too", insisting the government would not accept the current deal. Afghan leaders accuse the US of bestowing legitimacy on the Taliban, which has only emboldened them.
There is also mounting scepticism, now voiced by President Trump, that any commitments made by Taliban negotiators in Doha won't be upheld by commanders in the field
What does each side want?
Mr Trump pledged during the 2016 presidential campaign that he would end the US war in Afghanistan.
But he recently said that he wanted to get troop numbers down to 8,600 - about the same as the level when he entered office - and then "make a determination from there". He said the US would maintain a military presence in Afghanistan.
Many in Washington fear that a full US pull-out would leave the country deeply unstable and vulnerable to militant groups that could use it as a base to attack the West.
The Taliban militants now control more territory than at any time since the 2001 US invasion. They have insisted that they will not talk formally to the Afghan government until a timetable for the US troop withdrawal is agreed.
The initial US-Taliban deal was meant to pave the way for intra-Afghan talks on a broader political solution.
Some in Afghanistan fear that any deal could see hard-won rights and freedoms eroded and the Taliban back in power. The militants enforced strict religious laws and treated women brutally during their rule from 1996 to 2001.
Nearly 3,500 members of the international coalition forces have died in Afghanistan since the 2001 invasion, more than 2,300 of them American.
In a February 2019 report, the UN said that more than 32,000 Afghan civilians had died.
The Watson Institute at Brown University says 58,000 Afghan security personnel and 42,000 opposition combatants have been killed.