Ukraine's government will ask the UN's cultural watchdog to add the historic port of Odessa to its World Heritage List of protected sites as Russia's invasion continues, the agency said Tuesday.

Russian forces have advanced to within several dozen kilometres (miles) of the city, which blossomed after empress Catherine the Great decreed in the late 18th century that it would be Russia's modern gateway to the Black Sea.

Analysts say Russian President Vladimir Putin could soon target Odessa to completely block Ukraine's Black Sea access, potentially with heavy bombardments like those that razed the port of Mariupol.

In late July, the city was struck by missiles just hours after Russia agreed to allow a shipment of Ukrainian grain exports from the port.

"On July 24, 2022, part of the glass canopy and windows of the Museum of Fine Arts, inaugurated in 1899, were destroyed" by the strikes, the UNESCO cultural agency said after its director Audrey Azoulay met Ukraine's Culture Minister Oleksandr Tkachenko in Paris on Tuesday.

It said UNESCO experts already on the ground would provide technical assistance so that Odessa could be urgently added to both the World Heritage List and the list of heritage sites in danger.

It will also ask the World Heritage Committee to place the Saint-Sophia Cathedral in Kyiv and the historic centre of Lviv -- already recognised as UNESCO sites -- on the endangered list.

Adding a landmark site or traditional activity to the UNESCO list aims to mobilise attention to ensure it is preserved against threats to its existence.

The agency says 175 Ukrainian cultural and historic sites have been damaged since Russia launched its invasion in February, including monuments, museums, libraries and religious buildings.

Many were hit despite being marked with the distinctive "blue shield" indicating they are protected under the 1954 Hague convention on culture in armed conflicts, of which both Russia and Ukraine are signatories.

"The agency has already mobilised nearly $7 million and provided several aid measures and experts to advise professionals" working to protect sites or remove artworks to safer locations, UNESCO said.

In July, Ukraine also obtained recognition of the beetroot soup known as borshch on its list of intangible cultural heritage, which it said was under threat from Russia's invasion.