DIYARBAKIR, Turkey, Nov 29 (Reuters) - Thousands gathered for the funeral of Tahir Elci, a Kurdish lawyer and human rights activist gunned down on Saturday in a southern eastern city at the centre of months of violence.

The funerals for the two policemen killed in the attack in Diyarbakir also took place.

Prime Minister Ahmet Davutoglu said on Sunday the gun found next to Elci's body was the same weapon used in the attack on the police officers. He vowed to catch the killers.

Police surveillance camera footage released on Saturday showed policemen being shot at from inside a cab, falling onto the ground before the passengers ran on. Another video shows plain clothed police shooting at two men running in the direction Elci was believed to be standing.

Elci, who was shot after speaking to journalists, was facing trial for saying the banned Kurdistan Workers Party (PKK) was not a terrorist organisation, as the government describes it. He had, however, denounced PKK violence.

Hundreds of people have been killed since a ceasefire between the PKK and Turkish security forces collapsed in July, reigniting a conflict in which some 40,000 people have died since it began in 1984.

Elci's killing was likely to fuel further unrest in Turkey's mostly Kurdish southeast.

A curfew had been called in the Sur district of Diyarbakir where the killing took place and security forces conducted operations to drive back the youth wing of the PKK.

Deputies of the pro-Kurdish People's Democratic Party (HDP) and leaders of Turkey's local bar associations gathered at the funeral, where a casket draped in red, with bright yellow flowers was carried by a dense crowd.

Members of the Diyarbakir's Bar Association stood in front of the hospital from where the body was taken, holding a banned which said "We will not forget you," in Turkish and Kurdish.

Police dispersed protests against the killing using tear gas and water cannon in Istanbul on Saturday night.

(Reporting by Seyhmus Cakan in Diyarbakir and Humeyra Pamuk in Istanbul, writing by Dasha Afanasieva, editing by Ros Russell) ((dasha.afanasieva@tr.com; +90 212 350 7051;))