Russia has sought to defend its seven-month old war at the United Nations, with Foreign Minister Sergei Lavrov saying that regions of Ukraine where widely-derided referendums are being held would be under Russia's "full protection" if annexed by Moscow.

The referendums in four eastern Ukrainian regions, aimed at annexing territory Russia has taken by force since its invasion in February, entered their third day on Sunday and the Russian parliament could move to formalise the annexation within days.

Ukraine and its Western allies have dismissed the referendums as a sham designed to justify an escalation of the war and a mobilisation drive by Moscow after recent battlefield losses.

President Vladimir Putin on Wednesday ordered Russia's first military mobilisation since World War Two, a move that triggered protests across the country and sent flocks of military-age men fleeing, causing tailbacks at borders and sold-out flights from the country.

Russia's two most senior lawmakers on Sunday addressed a string of complaints about the mobilisation, ordering regional officials to get a handle on the situation and swiftly solve the "excesses" that have stoked public anger.

Addressing the UN General Assembly and the world's media in New York on Saturday, Lavrov attempted to justify Russia's invasion of its neighbour, repeating Moscow's false claims that the elected government in Kyiv was illegitimately installed and filled with neo-Nazis.

He cast opposition to what Russia calls a "special operation" as limited to the United States and countries under its sway. Nearly three-quarters of states in the assembly voted to reprimand Russia and demand it withdraw its troops.

In a news conference following his speech Lavrov said the regions where votes are underway would be under Moscow's "full protection" if they are annexed by Russia.

Asked if Russia would have grounds for using nuclear weapons to defend the annexed regions, Lavrov said Russian territory, including territory "further enshrined" in Russia's constitution in the future, "is under the full protection of the state".

Ukraine's foreign minister, Dmytro Kuleba, said Russia's mentions of the possible use of nuclear weapons were "absolutely unacceptable" and Kyiv would not give into them.