ISLAMABAD - A Pakistani Taliban breakaway faction that claimed responsibility for the bombing of a hospital last week said on Tuesday it had no links with Islamic State, whose leadership also said it was behind the attack.

Jamaat-ur-Ahrar, which briefly declared allegiance to Islamic State in 2014, said in an audio statement that its fight was solely against the Pakistani state and that linking it to trans-national militant networks was wrong.

"We want to make it clear that our movement has no connection to Daesh or Al-Qaeda," the group's leader, Omar Khalid Khorasani said, using the Arabic acronym "Daesh" to refer to Islamic State.

"Those in Daesh or Al-Qaeda or any other mujahideen movement are our Muslim brothers. But we do not have any organisational link with any of them.

With Daesh and Al-Qaeda we have never had an organisational link before, and even today we have no organisational link with them," Khorasani said.

Jamaat-ur-Ahrar claimed responsibility within hours for the suicide bomb in Quetta that killed more than 70 people, most of them lawyers, on Aug 8. Later, Islamic State, based in Iraq and Syria, also claimed responsibility.

That heightened fears that IS had gained a firmer foothold in Pakistan, a country of 190 million people where a myriad of local militant outfits exist with the means of launching major attacks.

Jamaat-ur-Ahrar, behind a series of bombings including in a public park in Lahore in March, has never specifically disavowed Islamic State before. Khorasani made no mention of the Quetta bombing in the audio message released on Tuesday.

In the statement, Khorasani said his group had no intention of fighting to install Islamic law beyond Pakistan. He also said that there were no Islamic State fighters present in the areas where his fighters were operating, largely along the lawless border with Afghanistan in Pakistani tribal areas.