The statement was issued by the militants on Sunday, a day after Malik made the remark. Malik had also said that the people should unite to root out terrorism as Pakistan was moving towards becoming a "durable peace".
The Taliban said people calling on the militants to declare a ceasefire should seek an end to air strikes in Pakistan's tribal areas.
"Have those asking us to take serious steps ever called for a halt to the bombing of tribal regions by the Pakistan Air Force and American drones?" demanded the statement issued by Taliban spokesman Ihsanullah Ihsan.
"We had offered peace talks in the national interest but secular elements did not like our serious offer and they have started making non-serious demands," Ihsan said.
Certain elements were describing the Taliban's offer of talks as a sign of weakness, he said. "Such remarks can force us into making a fearsome response," he warned.
The Taliban statement further called on the government to act quickly on its offer for talks as time was running out.
The militants have made several offers for talks to the government but Tehrik-e-Taliban Pakistan chief Hakimullah Meshud has made it clear that his fighters will not disarm.
The government has insisted that the militants should lay down arms and declare a truce before any talks.