The TTP aims to overthrow the government and replace it with a harsh brand of Islamic law.
01:54
Five Chinese engineers killed in suicide bomb attack in Pakistan
Five Chinese engineers killed in suicide bomb attack in Pakistan
Tahir said a mobile phone the suicide bomber had been using to communicate with his local handlers led to the arrest of the suspects.
The investigation and evidence show the militants had been taking instructions from TTP leaders in Afghanistan, he said.
Pakistani military had already said the attack was planned in Afghanistan and that the suicide bomber was also an Afghan national, a charge Kabul denies.
The TTP previously denied involvement and a spokesman said on Sunday that it had already explained its position on the attack.
“We have forensic evidence to prove that the TTP militants who were operating from Afghanistan are involved in it,” said Naqvi, the minister.
We want Afghanistan to act against these terrorists. Either try them there or hand them over to us
Kabul previously said rising violence in Pakistan is a domestic issue for Islamabad.
Relations between Pakistan and Afghanistan have soured in recent months. Islamabad says Kabul is not doing enough to tackle militant groups targeting Pakistan.
The minister said legal help will be sought from Kabul to arrest another three main members of the TTP who were directing the attacker and his facilitator from Afghanistan.
“We want Afghanistan to act against these terrorists. Either try them there or hand them over to us,” said the minister.