Pakistan was the expected venue for the meeting, due to take place on Friday, where Afghan officials had pledged to press the insurgents for a ceasefire.
A foreign ministry statement said the Afghan Taliban leadership had asked for the postponement “in view of the reports regarding the death of Mullah Omar and the resulting uncertainty”.
“Pakistan and other friendly countries of Afghanistan hope that the Taliban leadership will stay engaged in the process of peace talks in order to promote a lasting peace in Afghanistan,” the statement said.
Earlier on Thursday the Taliban distanced themselves from the talks, saying the movement’s political office was “not aware of any such process”.
The insurgents have not officially confirmed Omar’s death, and their comment on the talks casts doubt on the tenuous peace process.
The statement marked the first comment from the group, which has waged an almost 14-year insurgency against Afghan and foreign forces, since Kabul’s dramatic announcement on Wednesday citing “credible information” about Omar’s reported death.