"Now that US President Trump has announced the suspension of negotiations... this would not harm anyone else but the Americans themselves," the group said in a statement on Sunday.
In a series of tweets on Saturday, Trump said he was calling off secret meetings scheduled for Sunday with Taliban representatives and Afghan President Ashraf Ghani at Camp David in Maryland, US.
Citing a Taliban attack in Kabul last week in which 12 people, including a US soldier, were killed as the reason, Trump also cancelled the US-Taliban negotiations ongoing in Qatar for nearly a year.
The Taliban said the cancellation of talks would "lead to more losses for the US", "harm (its) credibility" and "show their anti-peace stance in (a) more clear way", Al Jazeera reported.
"Our struggle for the past 18 years... will continue until the foreign occupation is finished and the Afghans are given a chance to live by their own choice," said the statement.
The Taliban said the US negotiating team was "happy with the progress made so far" in Doha and the talks were held "in a good atmosphere".
"We had fruitful discussions with the US negotiating team and the agreement was finalized," said the statement.
The Taliban said it had even set September 23 as the inaugural day of another round of inter-Afghan dialogue in the hope that a deal with the US would be reached before that date.