A Russian air attack on Ukraine's southern port of Odesa early on Sunday killed one, injured nearly 20 and badly damaged an Orthodox cathedral, Ukrainian officials said, adding the icon of the patroness of the city had been retrieved from under the rubble.

"Odesa: another night attack of the monsters," Oleh Kiper, governor of the Odesa region, said on the Telegram messaging app.

One person was killed and 19 injured, including four children, in the missile attacks that also destroyed six houses and apartment buildings. Fourteen people were hospitalised, he said.

The Spaso-Preobrazhenskyi Cathedral, or the Transfiguration Cathedral, was severely damaged, Odesa's military administration said. Odesa's largest church building, it is located in the historic city centre, which is a UNESCO world heritage site.

The cathedral's archdeacon, Andriy Palchuk, told Reuters the missile strike had started a fire which only affected one corner of the cathedral containing non-historic religious artefacts for purchase by worshippers.

"When the right altar chapel - of the most sacred part of the cathedral - was hit, a missile piece flew through the whole cathedral and hit the area where we display icons, candles and books for purchase," he said.

Ukraine's defence ministry said the cathedral had now been "destroyed twice" - by Russian President Vladimir Putin and Soviet leader Joseph Stalin.

The early 19th-century cathedral was demolished in 1936 as part of Stalin's anti-religious campaigns and rebuilt when Ukraine gained independence from Moscow in 1991.

Parts of the building were destroyed, the floors were covered in rubble and chunks were ripped off the cathedral's ornate walls. Several local residents from the surrounding area came to assist with cleaning up the rubble.

Russia's Defence Ministry reported strikes on targets in the area but denied it had struck the cathedral and said the building had probably been hit by a Ukrainian anti-aircraft missile.

Russia has attacked Odesa with missiles and drones several times since it withdrew on Monday from a year-old deal that had allowed for safe exports of Ukraine's grain from Black Sea ports. Odesa's ports were the departure point for grain leaving Ukraine in the Turkey and UN-brokered agreement.

President Volodymyr Zelenskiy condemned Sunday's attack and vowed payback.

"There can be no excuse for Russian evil. As always, this evil will lose. And there will definitely be a retaliation to Russian terrorists for Odesa. They will feel this retaliation," he said on Twitter.

Italian Prime Minister Giorgia Meloni issued a statement condemning the attack and offering assistance in the reconstruction of the cathedral.

"The Russian aggressors demolish grain stores, depriving millions of hungry people of food. They devastate our European civilisation, its sacred symbols," she said.

In its daily briefing, Russia's Defence Ministry said it had struck targets "where terrorist attacks were being prepared" in the Odesa area and that all targets had been destroyed.

Separately, the ministry said Ukrainian reports of a Russian strike on the cathedral were false, and that its targets in Odesa were located "a safe distance" from the cathedral complex. It said that the "probable cause" of the damage to the cathedral was a Ukrainian anti-aircraft missile.

Russia has been pounding Odesa and other Ukrainian food export facilities nearly daily over the past week.

Pro-Kremlin military bloggers have said in the past week that Russia has changed its air attack tactics, using a combination of weapons in a "swarm" manner, one wave after another, which they say is more difficult to defend against.

Ukraine's air force said on its Telegram messaging app early on Sunday that Russia launched high-precision Onyx missiles and sea-to-shore Kalibr cruise missiles on Odesa.

The city's military administration said that air defence systems destroyed nine out of 19 missiles fired at Odesa and the surrounding region.

Russia has previously described its attacks on Odesa as revenge for a Ukrainian strike last week on a Russian-built bridge to Crimea, the Ukrainian peninsula that Moscow annexed in 2014. It has accused Ukraine of using the sea corridor to launch "terrorist attacks".

The cathedral that was hit on Sunday is of the Moscow-linked Ukrainian Orthodox Church (UOC) Ukraine's second-largest Church. Most Ukrainian Orthodox believers belong to a separate branch of the faith formed four years ago by uniting branches independent of Russian authority.

Ukraine has accused the UOC of maintaining links to the pro-invasion Russian Orthodox Church, which used to be its parent church but with which the UOC says it broke ties in May last year, following the Russian invasion.