Shelling hit southern Ukraine late on Saturday while Russia sought to defend its seven-month-old war at the United Nations even as it moves to escalate the conflict.

Kyiv and Western nations say referendums in territories Russia has seized by force are a sham designed to justify a ramping up of hostilities with newly drafted troops after battlefield losses in Ukraine in recent weeks.

Russian Foreign Minister Sergei Lavrov addressed the UN General Assembly and the world's press on Saturday, casting opposition to Russia's assault on its neighbour as limited to Washington and countries under its sway. Nearly three-quarters of countries in the assembly voted to reprimand Russia and demand it withdraw its troops shortly after the Feb 24 invasion.

Kyiv and Moscow traded blame for shelling in Ukraine's Zaporizhzhia region on Saturday.

Regional governor Oleksandr Starukh said on Telegram that Russian forces launched “a massive missile strike” on the region from about 10 planes, wounding at least three people.

Russia’s RIA state news agency, citing unnamed sources, said Ukrainian forces shelled a granary and fertiliser warehouses in the region.

Reuters was unable to verify either side's claims.

Lavrov, in a news conference following his speech to the assembly in New York, said the Ukrainian regions where votes are underway would be under Moscow's "full protection" if they are annexed by Russia, including with nuclear weapons.

The Group of Seven industrialised economies have said they will not recognise the results of the votes.

Ukraine requested an urgent UN Security Council meeting over the referendums, accusing Russia of violating the UN Charter by attempting to change Ukraine's borders, foreign affairs ministry spokesperson Oleg Nikolenko said on Twitter.

Putin on Wednesday ordered the country's first mobilisation since World War Two, an announcement that saw some Russian men headed swiftly to the borders, with traffic at frontier crossings with Finland and Georgia surging and prices for air tickets from Moscow rocketing.

More than 2,000 people have been detained across Russia for protesting the draft, including 798 people detained in 33 towns on Saturday alone, according to independent monitoring group OVD-Info.

Frustration has even spread to pro-Kremlin media, with one editor at the state-run RT news channel complaining that problems like call-up papers being sent to the wrong men were "infuriating people."

When asked on Saturday why so many Russians were leaving the country, Lavrov pointed to the right of freedom of movement.

- Reuters