"We must provide a clear signal that the world will not turn a blind eye to the destruction of our common history, our common culture, our common heritage," he told the 58 member states of the UN's cultural watchdog in a pre-recorded video.

"One of the steps for this should be the preservation of the historical centre of Odessa, a beautiful city, an important port of the Black Sea and a source of culture for millions of people in different countries."

Known as the pearl of the Black Sea, Odessa blossomed after empress Catherine the Great decreed in the late 18th century that it would be Russia's modern maritime gateway.

Czar Alexander named as governor France's Duc de Richelieu, who oversaw its construction and whose statue still stands atop its iconic Potemkin stairs.

But since Russia invaded Ukraine in February, Ukrainians have rushed to try to protect its monuments and buildings with sandbags and barricades.

"Odessa, like all other cities of Ukraine, is a target for Russian strikes," the Ukrainian president said.

"Please support Odessa! Show at the level of UNESCO precisely that Russian terror must end."

The UN cultural agency said Ukraine's application would be reviewed during the next World Heritage Committee meeting, without giving a date.

It said a place on the World Heritage List for Odessa "would recognise the exceptional universal value of this site and the duty of humanity as a whole to protect it".

"In legal terms, it would establish an extended protection zone" under the 1972 World Heritage Convention, it said.

Both Ukraine and Russia have signed the convention, which prohibits states from taking "any deliberate measures which might damage directly or indirectly the cultural and natural heritage" of others.

Six cultural sites in Ukraine are already inscribed on the UNESCO World Heritage List, including the Saint-Sophia Cathedral in the capital Kyiv and the historic centre of the western city of Lviv. None has so far made it on to the UNESCO List of World Heritage in Danger.

According to UNESCO, no Ukrainian cultural site on its World Heritage List has so far been hit in the war.

But Zelenskyy said Russian strikes had damaged 540 other "objects of cultural heritage, cultural institutions and religious buildings" since the invasion on February 24.