By Pinar Aydinli

ANKARA (Reuters) - Turkey took a step towards prosecuting Kurdish deputies accused of militant ties on Tuesday by seeking an end to their immunity, a move which could weaken Kurdish representation in parliament and fuel tension in the southeast.

Ten Kurdish MPs were accused of militant links after they were filmed in August embracing Kurdistan Workers Party (PKK) rebels, rifles slung over their shoulders, in images which provoked public outrage.

Turkey has been battling PKK militants near its southeastern borders with Iran, Iraq and Syria since they took up arms almost three decades ago to push for autonomy, in a conflict that has killed more than 40,000 people, mostly PKK members.

The PKK is designated a terrorist group by Turkey, the United States and European Union.

Kurdish members of parliament have been the subject of frequent investigations, accused of links to the militants, but are protected from prosecution while they are in office, unless the assembly votes otherwise.

Prime Minister Tayyip Erdogan said on Monday he favored lifting their immunity, and on Tuesday his office forwarded a request from state prosecutors to parliament seeking permission to investigate the 10 deputies, a senior official said.

All but one of them are members of the pro-Kurdish Peace and Democracy Party (BDP), which has 29 of 550 seats in parliament. If prosecutors are allowed to proceed, the charges they would face could carry jail sentences of five-10 years.

"Whether we are in prison or outside we will be involved in politics. We will stand by our people in their honorable struggle," said independent MP Aysel Tugluk, the only one of the 10 who is not a member of the BDP.

Others warned of serious consequences.

"If the parliamentary group collapses, it will mean Kurds being removed from parliament," said BDP deputy Nazmi Gur. "It will be down to (Erdogan's) AK Party and the prime minister."

NIGHT AT THE THEATRE

Erdogan has often taken an apparently contradictory approach on the Kurdish issue, maintaining a populist hard line in public but a more conciliatory stance behind the scenes.

On Monday evening, deputies from his AK Party and the BDP sat side by side at a performance of Shakespeare's Hamlet in Kurdish at a theatre in the capital Ankara - illustrating the growing acceptance of Kurdish culture under Erdogan's rule.

His latest comments appeared at odds with government signals that it was open to talks with the PKK after hundreds of its jailed members ended a hunger strike last week in response to an appeal from their leader.

He repeatedly dismissed the militants' hunger strike as a "show" and "blackmail", but his government rapidly sent to parliament a reform allowing defendants to use Kurdish in their court testimony, one of the protesters' demands.

During the same period he also mooted the idea of restoring the death penalty, expressing regret that it had been abolished, thereby saving jailed PKK leader Abdullah Ocalan from execution.

But at the same time, arrangements were made for Ocalan's brother to visit him in jail and pass on an appeal from the PKK leader which ended the hunger strike.

There are many prosecutors' requests concerning members of parliament from the BDP and other parties but parliamentary commissions have put them on hold until MPs finish their term.

It was not immediately clear whether the latest submission on the 10 Kurdish deputies would meet a similar fate.

Kurdish politicians, including those from the BDP, are frequently prosecuted for suspected links to the PKK, but deny ties with the militants. Previous Kurdish parties similar to the BDP have been closed down for such links.

(Writing by Daren Butler; Editing by Nick Tattersall and Alison Williams)