The Russian and Ukrainian special services have foiled a plot to assassinate Vladimir Putin immediately after Russia's presidential election next Sunday, state television reported.

Channel One said several men who were arrested in the Ukrainian Black Sea port of Odessa in January had been dispatched to kill Putin by the Chechen rebel Doku Umarov, the leader of Russia's separatist Islamist movement.

One of the men, identified as Ilya Pyanzin, was detained after an explosion in the Odessa flat he was renting with another man, who was reportedly killed in the blast. The television channel broadcast footage in which Pyanzin repeated what he said were the instructions he had been given. He said: "In Moscow you will sabotage economic sites. Further – an attempt on Putin."

Channel One also broadcast footage of the detention of a third man, identified as Adam Osmayev, a Chechen who was said to be living in London.

Bloodied and bare-chested, Osmayev told his interviewer: "The final goal was to go to Moscow and carry out an assassination attempt on Prime Minister Putin. The man who died was ready to become a suicide bomber."

The report also showed surveillance footage of Putin allegedly used by the men.

The security services of Russia and Ukraine did not comment on the report. Putin's spokesman confirmed it, but declined to comment further.

It was unclear why news of the arrests was not released sooner, but the announcement – which was made just one week ahead of an election that is expected to sweep Putin back into the Kremlin despite growing protests against his rule – was treated with suspicion in liberal circles in Moscow.

"Do I understand correctly that no one believes in the assassination attempt on Putin?" Danila Lindele, a leader of the opposition Blue Bucket movement, wrote on Twitter.

Another Russian user wrote: "It's better to pretend we believe it. Or else they'll start blowing up homes again."

Putin's critics allege that a series of apartment block bombings on the eve of his first election in 2000 were orchestrated by the Kremlin to boost the then unknown politician's popularity, rather than by Chechen rebels, as claimed.

A similar assassination attempt on Putin was allegedly foiled on the day of Russia's last presidential election in March 2008.