Ukrainian President Volodymyr Zelenskyy condemned a number of referendums being held in four occupied regions.
He also told those in Russian-controlled areas who have been conscripted into the army to “sabotage any activity of the enemy”.
Mr Zelenskyy added: “Do the main thing – save your lives and help us weaken and destroy the occupiers.”
Thousands are fleeing to avoid being sent to fight in Ukraine after the Kremlin declared a partial mobilisation. There are long queues of cars attempting to leave Russia at various border points – as men of fighting age attempt to avoid conscription.
Last Wednesday, Russian President Vladimir Putin announced a partial mobilisation of around 300,000 military reservists.
The BBC now reports there is a 10km queue at the border with Georgia.
Russia struck the Pechenihy dam on the Siverskyi Donets River in northeast Ukraine this week using short-range ballistic missiles or similar weapons, the British military said on Saturday.
The attack on Sept. 21 and 22 followed an earlier one on the Karachunivske dam near Krivyi Rih in central Ukraine on Sept. 15, the Defence Ministry said in its daily intelligence bulletin, adding that Ukrainian forces are advancing further downstream along both rivers.
Russian commanders may be attempting to strike sluice gates of the dams in order to flood Ukrainian military crossing points, the ministry said in its bulletin released on Twitter.
The attacks are unlikely to have caused significant disruption to Ukrainian operations due to distance between damaged dams and combat zones, according to the ministry.
In other developments:
* Ukrainian officials said people were banned from leaving some occupied areas until the four-day vote was over, armed groups were going to homes to force people to cast ballots, and employees were threatened with the sack if they did not participate.
* Reuters could not immediately verify reports of coercion.
* The votes in the provinces of Luhansk, Donetsk, Kherson and Zaporizhzhia were hastily organised after Ukraine recaptured large swathes of the northeast in a counter-offensive.
* Ukraine, Western leaders and the United Nations condemned the votes as an illegitimate precursor to illegal annexation. There are no independent observers, and much of the pre-war population has fled.
* The United States is prepared to impose additional economic costs on Russia in conjunction with U.S. allies if Moscow moves forward with annexing portions of Ukrainian territory, the White House said.
* NATO will ramp up its help for Kyiv in response to the “sham” referendums, the alliance’s secretary-general said.
* Russia maintains that the referendums offer an opportunity for people in the region to express their view.
* Russian attacked a dam on the Siverskyi Donets river with a suspected short-range ballistic missile, the second strike on a dam since Sept. 15, apparently with the aim of flooding Ukrainian military crossing points, British military intelligence said.
* A Russian missile hit a residential building in Zaporizhzhia causing casualties, the town’s acting mayor told media.
* A U.N.-mandated investigation commission said it had found evidence of war crimes including executions, rape, torture and confinement of children in Russian-occupied areas of Ukraine, after visits to 27 areas and interviews with more than 150 victims and witnesses.
* Russia denies deliberately attacking civilians in the conflict and says abuse accusations are a smear campaign. It did not immediately comment on the report.
* Ukraine said it would downgrade diplomatic ties with Iran over its decision to supply Russian forces with drones.
* The White House said the United States sees no reason to adjust its nuclear posture after Russia’s President Vladimir Putin’s warned the West he was not bluffing when he said he’d be ready to use nuclear weapons to defend Russia.