Putin said on Tuesday Russian troops would push further into Ukraine to build on their success on the battlefield after the weekend fall of the town of Avdiivka where he said Ukrainian troops had been forced to flee in chaos.

"Where should we stop? I don't know," former President Dmitry Medvedev, now deputy chairman of Russia's Security Council, said in an interview with Russian media. "We will have to work very hard and very seriously."

"Will it be Kyiv? Yes, it probably should be Kyiv. If not now, then after some time, maybe in some other phase of the development of this conflict."

Medvedev, once seen as a modernising reformer, has reinvented himself since the start of the war as an arch-hawk. He has issued a series of belligerent statements, assailing the West and warning of the risk of a nuclear apocalypse.

Russian troops were beaten back from Kyiv in the first weeks of the full-scale war that Putin launched in February 2022. They pose no current threat to the Ukrainian capital, though it has frequently come under missile and drone attack.

But Medvedev's comments appeared to reflect increasing confidence in Moscow about the course of the conflict. On the eve of its second anniversary, Ukrainian forces are outnumbered and outgunned by Russia's, and a major new package of aid for Kyiv has been held up in the U.S. Congress.

After the failure of Ukraine to pierce Russian front lines last year, Moscow has been trying to grind down Ukrainian forces just as Kyiv ponders a major new mobilisation and President Volodymyr Zelenskiy sacked his top general.

Medvedev said Russia also wanted to take the Black Sea port of Odesa, which it calls Odessa.

"Odessa, come home. We have been waiting for Odessa in the Russian Federation because of the history of this city, what kind of people live there, what language they speak. It is our Russian, Russian city," Medvedev said.

Russian forces expected a quick victory in 2022 but Ukrainian forces pushed Russian forces back later that year in a counteroffensive which showed serious problems in Russia's military.

Russia is now seeking to recapture the initiative across the 1,000 km (600-mile) front line, where its troops are dug in behind deep mine fields patrolled by drones and guarded by heavy artillery.

Russia currently controls a little under one fifth of territory internationally recognised to be Ukraine. Ukrainian President Volodymyr Zelenskiy says he will not rest until every last Russian soldier is ejected.

Russia says the territory its forces control is part of Russia and that it will never be given up. The West has committed about 250 billion euros ($271 billion) worth of aid to Ukraine in an attempt to defeat Russian forces.

Putin's suggestion of a ceasefire in Ukraine to freeze the war was rejected by the United States after contacts between intermediaries, Reuters reported exclusively earlier this month.

Ukraine and the West cast the war as an imperial-style land grab by Putin, and have warned that if Ukraine loses then Russia could attack a NATO member, something Putin has denied.

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(Reporting by Reuters)