Volodymyr Zelensky said it was a time for his country to be united, not divided. AFP

Ukrainian President Volodymyr Zelensky said Monday he doesn't believe it is the right time for elections as debate intensifies on holding a vote in 2024 while the country fights against Russia's invasion.

All elections including the presidential vote set to take place next spring are technically cancelled under martial law that has been in effect since the conflict began last year.

"We must decide that now is the time of defence, the time of battle, on which the fate of the state and people depends," Zelensky said in his daily address.

He said it was a time for the country to be united, not divided, adding: "I believe that now is not the (right) time for elections."

The frontline between the warring sides has remained mostly static for almost a year despite a much-touted Ukrainian counter-offensive, with Russian forces entrenched in southern and eastern Ukraine.

Officials from the United States and Europe -- Kyiv's key allies -- are reported to have suggested holding negotiations to end the grinding 20-month-old conflict.

But Zelensky has fiercely denied that Ukraine's counter-offensive has hit a stalemate, or that Western countries were leaning on Kyiv to enter talks.

The United States and other supporters have publicly maintained they are ready to back Kyiv with military and financial aid for as long as it takes to defeat Russia.

Global attention has turned to the Middle East since the October 7 Hamas attack on Israel -- and Zelensky has come under increasing pressure.

Russian strikes overnight in the southern Ukrainian region of Odesa left eight people wounded and damaged a historic art museum, Ukrainian officials said, in the latest barrage of drones and missiles.

Three more were injured in a Russian shelling attack on the southern city of Kherson on Monday, as Kyiv doubled down on its warnings that Russia was planning to pummel Ukraine's energy infrastructure ahead of the winter.

Images released by officials from inside the Odesa Fine Arts Museum showed art ripped from the walls of the 19th-century building and windows blown out by the aerial bombardment.

UNESCO said it "strongly condemns the attack" and that "cultural sites must be protected".

On Monday, Zelensky said that Ukrainian forces had successfully destroyed a major Russian ship in the Kerch shipyard in annexed Crimea.

The president, who was elected in 2019, said in September that he was ready to hold national elections next year if necessary, and was in favour of allowing international observers.

Voting could be logistically difficult due to the large number of Ukrainians abroad and soldiers fighting on the front.

Zelensky's approval rating skyrocketed after the war began, but the country's political landscape has been fractious despite the unifying force of the war.

Former presidential aide Oleksiy Arestovych has announced that he would run against his former boss, after criticising Zelensky over the slow pace of the counter-offensive.

Also on Monday, a close advisor to the commander-in-chief of the Ukrainian army, General Valery Zaluzhny, was killed by an explosive hidden inside a birthday gift.

"Under tragic circumstances, my assistant and close friend, Major Gennadiy Chastiakov, was killed," Zaluzhny wrote on Telegram, saying an investigation had been launched.

Ukrainian prosecutors meanwhile said they had formally notified two senior defence officials that they are suspects in a large-scale fraud case involving the purchase of military uniforms.

Ukraine has been fighting an uphill battle against systemic corruption as part of reforms urged by the West for membership to institutions like the European Union.

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