The Taliban offer of dialogue came in a statement addressed to the American people.
"Our preference is to solve the Afghan issue through peaceful dialogue," the Taliban said on Wednesday, while warning that their readiness to find peace should not be taken as a sign of weakness and that their armed campaign would be sustained no matter how powerful the US opposition is.
They said they didn't intend to damage any other country or let anyone use Afghan territory against anyone else.
"This can never mean that we are exhausted or our will has been sapped," they said.
In their statement, the Taliban did not mention a January 27 raid on the Kabul Inter-Continental hotel which left more than 30 people dead, nor a bomb attack on a crowded street a week later which left more than 100 killed. Previously, they claimed responsibility for both attacks.
Meanwhile, the spokesman for the Pakistani Taliban has also confirmed the death of their deputy leader in a recent US drone strike in Pakistan's northwestern tribal region.
A more aggressive US strategy in Afghanistan, including an increased number of air strikes launched by President Donald Trump in August, has pushed the Taliban back from several district centers and two provincial capitals.
Progress in preliminary talks has been obstructed by the deep mistrust between the government and the Taliban, as well as an ambiguity about the position of neighbors including Pakistan, which Afghanistan has long accused of aiding the insurgents.