ISTANBUL (Reuters) - Turkish prosecutors are investigating why the off-duty policeman who shot dead Russia's ambassador to Turkey was not captured alive, state media said on Wednesday, as the number of people arrested over the killing rose to 11.

Ambassador Andrei Karlov was gunned down from behind while delivering a speech in an Ankara art gallery on Monday. His killer was identified by Turkish authorities as Mevlut Mert Altintas, 22, who shouted "Don't forget Aleppo" and "Allahu Akbar" - Arabic for "God is greatest" - as he fired the shots.

Russian and Turkey both cast the attack as an attempt to ruin a recent thawing of relations chilled by the civil war in Syria, where they back opposing sides. The war reached a potential turning point last week when Russian-backed Syrian forces ended rebel resistance in the northern city of Aleppo.

The state-run Anadolu Agency said prosecutors were investigating why Turkish special forces, who stormed the gallery after the killing, did not take Altintas alive.

Initial findings suggest he continued to fire at police officers, shouting: "You cannot capture me alive!" Anadolu said. The officers shot Altintas in the legs, but he continued to return fire while crawling on the ground, it said.

President Tayyip Erdogan defended the police actions. "There is some speculation about why he wasn't captured alive. Look what happened in Besiktas when they tried to capture an attacker alive," Erdogan told reporters, referring to twin bombings this month outside the stadium of Istanbul's Besiktas soccer team.