Tehrik-e-Taliban Pakistan spokesman Ihsanullah Ihsan compared Malik to Pashto comedian Ismail Shahid and said the group did not take the minister's statements seriously.
"Our central shura (consultative council) believes that if Rehman Malik keeps on churning out statements about our offer (of talks), it'll indicate the government is not serious in pursuing peace talks," Ihsan told The Express Tribune.
"If the government replaces Rehman Malik with a serious person to deal with the dialogue issue, we will come up with an immediate, positive and civilised response in the best interests of Pakistan and its people," Ihsan said over phone from an undisclosed location.
Over the past few days, Malik has repeatedly ridiculed the Taliban's offer of peace talks, saying a dialogue can be held only if the banned group lays down arms and declares a month-long ceasefire.
On Saturday, Malik remarked that the Taliban raised the issue of talks whenever they were weak.
He also asked the group to name a team of "serious negotiators" if they wanted to make peace.
The Taliban spokesman said he has been stopped by his leaders from commenting on Malik's statements because the Taliban and "even many in Pakistan don't trust him".
Ihsan refused to comment on a conference of political parties convened by the Jamiat Ulema-e-Islam leader Maulana Fazlur Rehman later this month to discuss ways to end the conflict in Pakistan's northwest.
He also evaded a question about the possibility of tribal elders playing a role in the peace process.
"The Taliban are fighting for the existence of the tribal people as many tribesmen have been killed and displaced (by fighting in the region) and now they should have a better life," he said.