In a statement, Tehrik-e-Taliban Pakistan (TTP) spokesman Shahidullah Shahid said his group had no link with attacks on public places, "however, they could attack government places in our defence," Geo TV reported.
The banned group said "some elements" could launch attacks after it refused to extend the ceasefire.
As in the past, Taliban's doors were open for dialogue, he said and that if the government was serious, TTP could carry on talks.
The minister had stressed that talks cannot move forward without ceasefire. He had also rejected Taliban claims that government is not serious in pursuing peace talks with it.
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The Taliban which had called off its ceasefire on Wednesday, has put the blame on the government saying it was not serious about talks.
Official sources quoted the minister as saying that the government has removed all blocks on the road to dialogue with sincerity and strong resolve.
Sharif's government had begun negotiations with the Taliban through intermediaries in February to try to end the decade-long cycle of violence that has claimed over 40,000 lives.