The body of a 42-year-old man with "gunshot wounds" was found on Monday morning, the Investigative Committee, which probes serious crimes, said in a statement later in the day.

The man worked as the deputy to the Krasnodar city administration official in charge of "mobilisation operations" for the army, they said.

Investigators said they were seeking to identify the person behind the incident and establish a possible motive.

According to the Russian state-run news agency TASS, citing police sources, the victim was Stanislav Rzhitski.

Russian MP and former mayor of Krasnodar, Yevgeny Pervychov, said on Telegram Rzhitski served in the navy, where he was notably commander of the "Krasnodar" submarine.

Rzhitski was killed while out for a jog, according to Russian Telegram outlet Baza.

Since April, the Russian army has been conducting a vast military recruitment operation, running massive advertising campaigns, promising big salaries and other perks.

The aim of the drive is to replenish forces on the frontline in Ukraine, without resorting to another mobilisation -- a step that the Kremlin took last September which proved unpopular.

In a sign of a degree of hostility towards the conflict, dozens of people have been arrested and accused of setting fire to -- or planning to set fire to -- recruitment centres since the beginning of the offensive in Ukraine.