ISTANBUL (Reuters) - Turkish President Tayyip Erdogan has said he backs a criminal investigation into leaders of the pro-Kurdish opposition over comments about Kurdish self-rule, saying those who committed constitutional crimes must pay the price.

Turkish President Tayyip Erdogan attends the opening session of the World Climate Change Conference 2015 (COP21) at Le Bourget, near Paris, France, November 30, 2015. REUTERS/Christian Hartmann

A Turkish prosecutor opened an investigation into Selahattin Demirtas, co-head of the pro-Kurdish Peoples’ Democratic Party (HDP), last week after a two-day congress of Kurdish groups called for greater self-governance.

The probe comes as predominantly Kurdish southeast Turkey experiences some of its worst violence since the 1990s after a two-year ceasefire between Kurdish militants and the state collapsed in July.

“The statements of the HDP leaders are constitutional crimes. There are investigations started by prosecutors against them. These should be followed up,” Erdogan told reporters in comments published by the Hurriyet newspaper on Saturday.

“I believe the process that will start with the removal of immunities will have a positive impact on the mood of our country in fighting terrorism,” he said.

As members of parliament, Demirtas and other HDP leaders would normally enjoy immunity from such cases, although they could be prosecuted and have the sentence suspended until a time when they no longer have immunity.

Erdogan urged parliament last July to lift the immunity of politicians with suspected links to militants, after a prosecutor launched an investigation into Demirtas over accusations he “provoked and armed” protesters.

The Kurdistan Workers’ Party (PKK) first took up arms in 1984 to push for greater autonomy in the southeast, and some 40,000 people have been killed in the violence. It is designated a terrorist group by the United States and European Union.

Erdogan said on Thursday there would be no let-up in a military campaign that he said had killed more than 3,000 militants last year.

Demirtas has said the campaign is targeting local people who are presented as “terrorists”, a charge the government denies.

The HDP said on Saturday that around 1,000 people were trapped in the Zap district of Silopi province in the southeast, many sheltering in the basements of their houses, as the area came under tank fire. Television footage also showed smoke billowing from buildings under tank fire in the nearby district of Cizre.