By Daren Butler

ISTANBUL (Reuters) - Turkish Prime Minister Tayyip Erdogan has signaled that new talks with Kurdish militants might be possible as his government contends with an upsurge in separatist violence in the country's southeast.

The conflict has cost Turkey dearly since the militants took up arms in 1984, both in human and economic terms, and as the death toll climbs there is growing public pressure on Erdogan to bring an end to the bloodshed.

Turkish intelligence officials have had contact with senior figures from the Kurdistan Workers Party (PKK) in the past few years to try to end a conflict that has claimed more than 40,000 lives, but discussions have broken down.

"Regarding Imrali, there could be more talks," Erdogan said in a televised interview with broadcaster Kanal 7 late on Wednesday, referring to the small island where PKK leader Abdullah Ocalan is serving a life sentence.

"There is a military dimension to this, a security dimension which is separate and will continue. But beside this there is a diplomatic, socio-economic and psychological dimension."

Erdogan spoke after Turkey's main pro-Kurdish party called for the resumption of talks between the state and the PKK to prevent a further escalation of violence.

Clashes in the past several months between Turkey's armed forces and militants from the PKK - considered a terrorist organization by Ankara, the United States and European Union - have been among the heaviest since the conflict began.

Turkish soldiers backed by helicopters killed 13 PKK fighters on Thursday during clashes in Cukurca near the mountainous Iraqi border, security sources said. Two soldiers were killed and three wounded in the fighting.

Ankara has linked the surge in violence to the unrest in neighboring Syria. Erdogan has accused President Bashar al-Assad of arming the PKK militants and raised the possibility of military intervention in Syria if the PKK were to launch attacks from Syrian soil.

MILITARY TARGETS PKK LEADERS

The head of Turkey's armed forces said in a newspaper interview on Wednesday that the military also had the capability to launch a sustained operation against the PKK in northern Iraq.

Erdogan gave his interview a few days before his AK Party's congress, where he is expected to set out the party's future as it goes through its biggest overhaul since coming to power a decade ago.

Since elections in June 2011, the conflict with the PKK has killed more than 700 people, according to the International Crisis Group - the highest toll in a 15-month period since Ocalan was jailed in 1999.

Turkish special forces captured Ocalan in Kenya that year after Assad's father, then-President Hafez al-Assad, cast him out of Syria amid concern that Turkey would launch military action over the militant leader's presence in Damascus.

Since his conviction, Ocalan has been jailed on the island of Imrali, located in the Marmara Sea south of Istanbul.

(Additional reporting by Seyhmus Cakan in Diyarbakir; Editing by Nick Tattersall and David Goodman)