* Turkish jets reportedly bomb rebel positions in N.Iraq
* Thousands gather for arrival of slain activists' bodies
* Funerals of activists on Thursday, Erdogan urges calm (Adds arrival of activists' bodies in Diyarbakir, policeman killed in Mardin)
By Jonathon Burch and Daren Butler
ANKARA/DIYARBAKIR, Turkey, Jan 16 (Reuters) - Turkish Prime Minister Tayyip Erdogan said on Wednesday military operations against Kurdish rebels would continue until they laid down their arms, as Turkish media reported warplanes had bombed militants in northern Iraq for a third day.
The prospect of an end to three decades of war between the Turkish state and the Kurdistan Workers Party (PKK) has gained momentum in recent weeks after the government acknowledged it was talking to the insurgents' jailed leader.
Erdogan, under pressure to bring an end to the violence, has said his government's renewed peace efforts are sincere but has also maintained Ankara's hardline rhetoric over a conflict that has burned for 30 years.
"We want a solution with all our hearts, but to achieve this we will never compromise our dignity," Erdogan told members of his ruling AK Party at their headquarters in Ankara.
"Until the terror organisation lays down its arms, until they end their attacks, our security forces will continue their operations," he said, describing the nascent peace talks as a "test of sincerity".
Turkish warplanes bombed PKK targets in northern Iraq overnight, according to media reports. Broadcaster CNN Turk said on Tuesday jets had also attacked PKK forces there on Sunday and Monday, in the first such raids since details of talks with PKK leader Abdullah Ocalan emerged.
Firat news agency, which has close links to the PKK, reported on Wednesday seven PKK fighters had been killed this week in air strikes.
There was no official Turkish confirmation of the raids.
Turkey is still reeling from one of the most violent summers since the PKK, which is designated a terrorist group by Ankara, the United states and the European Union, took up arms against the state in 1984. More than 40,000 people, mostly Kurds, have been killed since then.
Late last year Turkish intelligence officials began talks with Ocalan, imprisoned on an island south of Istanbul. Those talks have drawn fierce criticism from nationalist circles which accuse the government of going soft on the PKK.
The discussions were overshadowed last week by the execution-style killings of three Kurdish women activists in Paris, which Erdogan has suggested could be the result of an internal feud in the PKK or a bid to derail the peace moves.
ACTIVISTS' BODIES FLOWN HOME
The bodies of the activists, including that of PKK co-founder Sakine Cansiz, arrived by plane on Wednesday evening in Diyarbakir, the largest city in Turkey's mainly Kurdish southeast, ahead of a funeral ceremony on Thursday.
Amid tight security, thousands of Kurds gathered peacefully outside the airport, holding up pictures of Cansiz and chanting slogans in support of the PKK.
"Martyrs are immortal!", "Kurdistan will be a grave for fascism!" and "Long live leader Apo!" they shouted, referring to Ocalan, as vans carrying the coffins draped in green cloth drove slowly through the crowd.
Erdogan repeated his and other political leaders' call on Wednesday for calm at the funerals and said security forces would be "extremely sensitive and vigilant" against any provocation or sabotage.
Erdogan's government has widened cultural and language rights for Kurds, who make up about 20 percent of Turkey's population, since taking power 10 years ago. Kurdish politicians say the reforms do not go far enough.
While spelling out its demands from the insurgents, the government has given little hint of what concessions, if any, it might be willing to make. The PKK, like most Kurds in Turkey, still see "political autonomy" as one of their main demands in any solution to the Kurdish problem.
Underscoring the ongoing violence in Turkey's volatile southeast, PKK fighters attacked a police vehicle on Wednesday in the city of Mardin, southeast of Diyarbakir, killing one policeman, security sources said. (Additional reporting by Gulsen Solaker in Ankara and Seyhmus Cakan in Diyarbakir; Writing by Jonathon Burch)