"Afghanistan seeks good diplomatic relations with all neighbours, including Pakistan", spokesperson Zabihullah Mujahid said in a statement released on Tuesday.
The Taliban spokesperson termed "good diplomatic ties" between the two countries as "crucial".
Though Mujahid vowed that Afghanistan would "not allow its land to be used" for militancy and to destabilise a neighbouring country, he demanded Pakistan take steps to "control unrest, militancy, and law and order situation" in its own territory first.
A day earlier, the Taliban regime in Kabul had reacted angrily to Interior Minister Rana Sanaullah over his remarks that Pakistan could carry out cross-border military action against the outlawed TTP, which was using its safe havens in Afghanistan to perpetrate its terror campaign.
“Afghanistan is our brotherly country and we will first talk to them to dismantle the TTP hideouts… but if they don’t then the international laws give you the right to target those who attack you,” Sanaullah was quoted as saying while talking to Express News.
In its response, the Taliban's interim "Ministry of National Defense" had said it considered the claim about the presence of TTP in Afghanistan “provocative and baseless”.
Some 420 terrorist attacks have been recorded since the Taliban takeover in Pakistan's neighbouring country of Afghanistan; the banned TTP claimed responsibility for 141 of them.