After nearly half a year of purges in Turkey’s security forces after a failed military coup, the assassination of the Russian ambassador by a vetted Turkish police officer suggests that President Recep Tayyip Erdogan may face a resilient disloyalty problem.

Within hours of the assassination on Monday in Ankara, Turkish officials and the pro-government news media portrayed the gunman as a sleeper-agent disciple of Fethullah Gulen, a Muslim cleric who commands a following in the country and is accused of having directed the July 15 coup attempt to topple Mr. Erdogan.

But it was also possible that the assassin, identified by the authorities as a 22-year-old riot police officer, Mevlut Mert Altintas, might have been a follower of the Nusra organization, linked to Al Qaeda, or of the Islamic State. Those extremist groups have used Turkey as a transit point into Syria and have battled Russia in the war there. The gunman shouted jihadist slogans invoking Syrian victims of Russian attacks as he fired bullets into the ambassador, Andrey G. Karlov, before being killed by fellow officers.

Political analysts said that regardless of Mr. Altintas’s affiliation — with Gulenists, Islamists or some other group — the assassination at an art gallery in Turkey’s capital betrayed a glaring unknown among forces that have pledged fealty to Mr. Erdogan.