The Taliban says Americans have the most to lose from cancelling peace negotiations that sought to end the 18-year war in Afghanistan.
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.
US President Donald Trump had 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.
The US currently has about 14,000 troops in Afghanistan.