Turkey's parliament will set up a committee to consider lifting the immunity of two leaders of the main Kurdish party so they can be tried over their call for autonomy, the pro-government Sabah daily said Sunday.

The report came after President Recep Tayyip Erdogan said Selahattin Demirtas and Figen Yuksekdag -- the co-leaders of the Peoples' Democratic Party (HDP) -- should have their parliamentary immunity removed for committing a "constitutional crime".

Sabah said that the parliamentary justice commission would form a sub-committee to discuss the issue before putting it to the general chamber.

A simple majority to strip the two MPs of their immunity would suffice in parliament, where the ruling Justice and Development Party (AKP) holds more than half the seats, it added.

Turkish prosecutors last week opened a criminal probe against Demirtas for his comments at a conference and then opened a similar investigation against Yuksekdag.

Demirtas said last weekend that the Kurdish minority in Turkey had to decide whether to live in autonomy or "under one man's tyranny", in an apparent reference to Erdogan.

The AKP's deputy chairman Selcuk Ozdag told the Hurriyet daily that anyone who "damaged the integrity of the country, supported terror or who hurts unity" should have no immunity.

"It does not matter which party someone is from: immunity should not be used as a shield against criminal proceedings over grave crimes," he added.

"No-one should have the freedom to commit crimes... the HDP has already overstepped the mark," he said.

Demirtas meanwhile hit out at Erdogan's comments, accusing the Turkish strongman of "giving out verdicts like the supreme court", the Dogan news agency reported.

The probe comes amid rising tension between the authorities and many in the Kurdish minority over the military's relentless campaign -- backed by curfews -- against rebels from the Kurdistan Workers' Party (PKK) in the southeast.

Demirtas' remarks outraged nationalists who believe any degree of autonomy for Turkish Kurds in the southeast would undermine the unitary nature of the modern Turkish state set up by Mustafa Kemal Ataturk in 1923.

Several pro-Kurdish mayors in towns throughout the southeast have already been investigated since the summer on similar charges.

According to pro-Kurdish media, 36 mayors are currently being prosecuted with half of them in custody.