Ukraine has offered Russian soldiers money and promised them immunity from punishment if they surrender.
"Make your decision. Come out without weapon, with white flag," Defence Minister Oleksii Resnikov wrote on Facebook on Tuesday night.
Each soldier is being offered the equivalent of more than €40,000. The campaign is reportedly being financed by the international IT industry.
"Anyone who refuses to be an occupationist will bring peace. For those who choose the path of the occupationist - there will be no mercy!" said Resnikov.
Whether surrendering Russians will actually receive the money could not be verified.
According to Ukrainian sources, at least 200 Russian soldiers have been captured so far.
In interrogation videos, many have said they believed they were taking part in a manoeuvre - but were actually sent to fight in Ukraine.
Russia attacked the neighbouring country last Thursday without declaring war.
According to the UN, more than 100 civilians have already been killed, while more than 300 have been injured.
Up to the early hours of Tuesday, the Russian army had already fired at least 113 ballistic missiles at Ukraine, according to Ukrainian sources. Moscow vehemently denies attacking Ukrainian civilians.
The Ministry of Defence in Kiev said more than 5,700 Russian soldiers had been killed by Tuesday morning. Again, these figures cannot be independently verified.
Meanwhile, Ukraine listed some 29 aircraft, 29 helicopters and 198 tanks among allegedly destroyed Russian military equipment.