Kyiv's western allies have dismissed as a sham the referendums in the eastern Donetsk and Lugansk regions, as well as in the southern Kherson and Zaporizhzhia regions.
US President Joe Biden vowed "swift and severe" costs if Russia followed through and annexed the regions.
Even China, Russia's closest ally since the war began, acknowledged to Kyiv that the "sovereignty and territorial integrity of all countries must be respected".
Chinese Foreign Minister Wang Yi made the comments to his Ukrainian counterpart Dmytro Kuleba at the UN General Assembly on Friday.
Authorities in the Russian-controlled regions are going door-to-door for four days to collect votes. Polling stations then open Tuesday for residents to cast ballots on the final day of voting.
It was also possible to vote at the building in Moscow that represents the Donetsk breakaway region.
Leonid, a 59-year-old military official, told AFP he was "feeling happy".
"Ultimately, things are moving towards the restoration of the Soviet Union. The referendum is one step towards this," he said.
But earlier this month, a Ukrainian counter-offensive seized back most of the north-eastern Kharkiv region, bringing hundreds of settlements back under Kyiv's control after months of Russian occupation.
And on Friday, Kyiv said its forces had made more progress, recapturing a village in the Donetsk region and retaking positions south of the war-scarred town of Bakhmut.
The four regions' integration into Russia would represent a major escalation of the conflict as Moscow would consider any military move there as an attack on its own territory.
The referendums are reminiscent of the one held after Russia's annexation of Ukraine's Crimea in 2014, which was also denounced by Western nations.
Evidence of 'war crimes
In his evening address Friday, Ukrainian President Volodymyr Zelensky denounced the polls as "pseudo-referendums" expressing confidence that the world would reject them.
Biden's statement on Friday backed that position.
"Russia's referenda are a sham -- a false pretext to try to annex parts of Ukraine by force in flagrant violation of international law," said Biden.
"We will work with our allies and partners to impose additional swift and severe economic costs on Russia."
Earlier Friday, the G7 Group of Seven industrialised nations condemned the referendums as a "sham" with "no legal effect or legitimacy".
In Donetsk and Lugansk -- which Putin recognised as independent just before invading Ukraine in February -- residents are answering if they support their "republic's entry into Russia", TASS reported.
Ballots in Kherson and Zaporizhzhia ask the question: "Are you in favour of secession from Ukraine, formation of an independent state by the region and its joining the Russian Federation as a subject of the Russian Federation?"
Russian news agencies reported that voting had begun on Friday at 0500 GMT, while TASS reported paper ballots would be used to save time.
UN investigators meanwhile said Friday that war crimes had been committed in the Ukraine conflict, listing Russian bombings of civilian areas, torture, horrific sexual violence and a "large number of executions".
In eastern Kharkiv region, Ukrainian officials said Friday they had finished exhuming 447 bodies from a site near the city of Izyum.
"Most of them have signs of violent death, and 30 have signs of torture," said Kharkiv regional governor Oleg Synegubov in a post on social media.
"There are bodies with rope around their necks, with their hands tied, with broken limbs and gunshot wounds," he added. Izyum was part of the territory recently recaptured from Russian forces.
The Kremlin has accused Kyiv of fabricating evidence of the alleged war crimes.
Tomorrow you will go to war
Putin this week warned that Moscow would use "all means" to protect its territory -- which former Russian leader Dmitry Medvedev said on social media could include the use of "strategic nuclear weapons".
Moscow began its mandatory troop call-up on Thursday after Putin called for about 300,000 reservists to bolster the war effort.
But men were leaving Russia in droves before they were made to join, with flights to neighbouring countries booked up for days to come.
Some however have not been able to avoid the summons.
Mikhail Suetin, 29, was among those detained at an anti-mobilisation protest in Moscow this week and was handed a summons to appear at a recruitment office.
"To be told 'tomorrow you will go to war'... that was a surprise," Suetin, who regularly joins opposition protests in Moscow, told AFP.