* Killings cast shadow over nascent peace process
* Leading Kurdish politician says it's time for peace
* Turkish prime minister urges calm
* European Committee for Prevention of Torture visits Ocalan (Adds quotes, details, background)
By Daren Butler
DIYARBAKIR, Turkey, Jan 17 (Reuters) - Tens of thousands of Kurds poured onto the streets of the Turkish city of Diyarbakir on Thursday for the funeral of three Kurdish activists killed in Paris, chanting slogans as coffins passed through the crowds.
The three women, including a co-founder of the outlawed Kurdistan Workers Party (PKK), died last week in execution-style shootings which many saw as an attempt to derail a nascent peace process between Ankara and the guerrillas after three decades of conflict.
Hopes of an end to the war have grown in recent weeks after the government acknowledged it was talking to jailed PKK leader Abdullah Ocalan.
Diyarbakir's Baglar district, a PKK stronghold, drew massive crowds as the coffins, draped in green cloth and decorated with red carnations, were loaded onto hearses and driven slowly through the streets.
The bodies of PKK member Sakine Cansiz and the two other activists arrived in Turkey's main Kurdish city amid tight security late on Wednesday.
"The martyrs' path is our path. PKK is our party! Long live leader Apo!" the crowd chanted, referring to Ocalan, jailed on an island south of Istanbul since his capture in 1999.
Headscarved women and children applauded and waved, while others made victory signs from the windows of apartment blocks. Two young men, their faces concealed by scarves, held aloft the green, red and yellow flag of the PKK.
"OUR HEARTS ARE BURNING"
Thousands more waited for the bodies to arrive at a parade ground where the funeral ceremony was to take place before the bodies were taken for burial in the women's hometowns.
The crowds surged towards the coffins, now draped in the PKK colours, while female relatives and friends touched the caskets and wept. Photos of the women were placed by the coffins.
"Our hearts are burning. Three beautiful youths were slaughtered monstrously. Our three comrades were slaughtered just because they wanted freedom, an honourable life," said a tearful Aysel Tugluk, a senior lawmaker from the pro-Kurdish Peace and Democracy Party (BDP), struggling to talk.
There were minor scuffles between some groups and police fired water cannon to disperse them, but no serious violence. Prime Minister Tayyip Erdogan had urged calm at the funeral and said security forces would be "sensitive and vigilant".
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 approach to a conflict that has burned for almost 30 years.
Turkish warplanes bombed PKK targets in northern Iraq this week, according to media reports, in the first such raids since details of the talks with Ocalan emerged. The country is still reeling from one of the most violent summers of the conflict.
More than 40,000 people, mostly Kurds, have been killed since the PKK, designated a terrorist group by Turkey, the United States and the European Union, took up arms in 1984.
Efforts to begin a peace process were overshadowed last week by the Paris killings, which Erdogan has suggested could stem from an internal PKK feud or a bid to spoil the talks. The PKK blamed elements within the Turkish state or foreign powers.
Addressing crowds in Diyarbakir, BDP Co-chairman Selahattin Demirtas said the Paris killings should be a watershed.
"We say now is the time for peace. We shout this out in front of the bodies of our dead. Don't let our children die any more. We can stop this bloodshed by talking. Through discussions we can solve our problems," Demirtas said.
"If the process is to advance with confidence, these murders must be a turning point."
Erdogan's government has widened cultural and language rights for Kurds, who make up about 20 percent of Turkey's population of 71 million, since it came to power 10 years ago but Kurdish activists say the reforms do not go far enough.
The government has spelt out its demands but given little hint of what concessions, if any, it might be willing to make. The PKK, and most Kurds, want greater autonomy.
Kurdish politicans have called for improved prison conditions for Ocalan. A Turkish official confirmed on Thursday a delegation from the European Committee for the Prevention of Torture (CPT) had visited the PKK leader on Wednesday and were meeting Turkish prosecutors on Thursday.
The official described the visit, the first by the committee since 2010, as "ad-hoc", but gave no further details. Turkey had the right to keep the committee's subsequent report of the visit confidential, the official said, but Ankara had in the past always chosen to make it public.
Many Turks oppose greater Kurdish autonomy, fearing it is a slippery slope towards a separate Kurdish state, and favour a hardline military response to the PKK.
Local media has largely been muzzled in its coverage of the conflict, and the large turnout in Diyarbakir for the funerals received only brief mentions on mainstream television channels.
But there are signs of Ankara's stance softening.
"Turkey is still at the beginning of a very important process ... I believe we all carry a responsibility in this process," said Deputy Prime Minister Bulent Arinc on Thursday. (Additional reporting and writing by Jonathon Burch in Ankara; Editing by Andrew Roche)