The group had proposed a "conditional dialogue" to the previous government led by the Pakistan People's Party in February but withdrew the offer after it did not receive a "positive" response.
"If they (the new government) take our dialogue offer seriously and makes some progress, then we could also stop attacks," Ihsan said by phone from an undisclosed location.
The incoming Prime Minister, PML-N chief Nawaz Sharif, said this week that the Taliban's offer for dialogue would be taken seriously.
"We have seen Nawaz Sharif's reported remarks and respect his statement about our dialogue offer," Ihsan said.
"I would reiterate that we are serious in our dialogue offer but the outgoing rulers had adopted a non-serious approach," he claimed.
"The Tehrik-e-Taliban Pakistan does not declare a ceasefire now and any such decision would depend on the new government's approach."
Ihsan further said: "I cannot say now that we are stopping attacks but there could be a possibility of stopping attacks as a goodwill gesture once the new government takes some serious steps."
The Taliban repeatedly targeted the PPP and its secular-leaning allies - the Awami National Party and the Muttahida Qaumi Movement - before the general election and forced the three parties to dramatically curtail their campaigning.
Over 200 people were killed during the campaign period and the election day in a string of bombings and attacks by militants.