The move by cricketer-turned-politician Imran Khan's Tehreek-i-Insaaf (Movement for Justice) party is set to put the government under added pressure as it fights a major corruption case against Prime Minister Nawaz Sharif.
Last week a report by Supreme Court Justice Qazi Isa into a suicide bombing of a hospital in August that killed 73 people strongly criticised the government for failing to implement anti-terror policies.
It singled out Interior Minister Chaudhry Nisar Ali Khan for holding meetings with cleric Maulana Muhammad Ahmed Ludhianvi.
The two groups jointly also claimed an attack on a police academy in October that killed 61 people and one on a shrine that killed 52 in November. All three attacks were in the southwestern province of Balochistan.
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"The report has raised the issue of the Interior Ministry inviting and holding meetings with leaders of banned militant organisations," a statement by Imran Khan's party said.
The speaker of parliament will now decide whether to accept the request for a special meeting to debate the report.
Overall levels of violence have decreased in Pakistan since the army stepped up operations in the border regions and major cities in the wake of a Taliban school massacre of more than 150 people, mostly students, in December 2014.
But the judge's report said the government had a long way to go.
"Proscribed organisations continue their illegal activities and new terrorist organisations are proscribed after long delays," it said.
The resurgence of Lashkar-e-Jhangvi in the southwest, together with its links to the Islamic State group, are a major blow to long-running and partly successful efforts to quell a homegrown Islamist insurgency that sprang up in the aftermath of the 2001 invasion of Afghanistan.