With Russian forces pushing deeper into their country, Ukrainians are scrambling to safeguard a rich cultural history that experts warn could be deliberately targeted in a bid to force Kyiv into submission.

Museums have rushed to remove collections to safer storage, and in many churches stained-glass windows have been boarded up or altars removed entirely.

In the southern port city of Odessa, sandbags have been piled up in front of the statue honouring the French Duke of Richelieu, a governor under the Russian emperor Alexander I.

But many sites have already been damaged or destroyed by Russia's bombardments of city centres, which have also hit schools, hospitals and other civilian structures.

The mayor of the northern city of Chernihiv posted a video Friday of a library reduced to rubble by shelling, heightening fears of indiscriminate targeting.

The UN cultural agency UNESCO is helping local officials mark sites with the distinctive blue-and-white shield, hoping that Russia will honour the 1954 Hague Convention for the protection of cultural heritage during armed conflicts, of which it is a signatory.

"We call on all states to respect the international law they have signed and therefore not to target important sites in the country," Lazare Eloundou, director of UNESCO's World Heritage programme, told AFP at the agency's headquarters in Paris.

He warned of extensive damage already to museums and other cultural venues and monuments, some dating back to the 11th century.

"It is a whole cultural life that risks disappearing," Eloundou said.

Statues covered with protective wrappings at the Latin Cathedral in Lviv, western Ukraine
Statues covered with protective wrappings at the Latin Cathedral in Lviv, western Ukraine AFP / Yuriy Dyachyshyn

The capital city of Kyiv itself is a World Heritage Site, with the Saint Sophia Cathedral and the Lavra monastic complex that were key to the development of the Russian Orthodox Church.

Lviv in the west is also among the several UNESCO heritage sites in Ukraine, which has more than a dozen others that are candidates for the list, which would encourage their protection.

Officials hope that by clearly marking the sites Russia's armed forces will be forced to face trial if they are targeted, similar to the 2016 conviction of a Malian jihadist for destroying heritage mausoleums in Timbuktu.

"If we do everything to protect our heritage, then Russia is going to pay for all the evil, for any destruction of any cultural site," said Olga Ganenko of Ukraine's UNESCO delegation.

Yet many fear Russia will not hold back, and that marking buildings and monuments with the UNESCO shield might even be counter-productive.

"They will become the deliberate target for the Russian aggressor, who ignores all international laws," said Ihor Poshyvailo, director of the Maidan Museum in Kyiv, who is coordinating a citizens' initiative to protect Ukraine's cultural sites.

"They want to destroy our historical memory, our cultural identity as a nation," he said, referring to the irredentist "greater Russia" ambitions allegedly harboured by Russian President Vladimir Putin.

Those fears are shared by Jasminko Halilovic, director of the War Childhood Museum in Sarajevo, set up after the 1992-1995 Bosnian War and which now has an outpost in Kyiv.

"If you are trying to destroy a community or society, one of the things you will definitely target is the cultural heritage... because it tells us who they were before and who they are yet to become," he said.

"If one side is attacking schools and hospitals, then it is very unreasonable to expect that they would care about cultural heritage," he added.