Putin 'planning mass intrusion into Ukraine' says Saakashvili
Mr Zelensky issued the offer to his Kremlin counterpart in a video message posted on the Kiev government's presidential website. It comes amid growing fears of an all out Russian attack on Ukraine after Moscow ordered more than 120,000 troops to the border.
Volodymyr Zelensky has invited Vladimir Putin to peace talks in Ukraine
I am ready to go even further and invite you to meet anywhere in the Ukrainian Donbass
Mr Zelensky said: "Mr Putin: I am ready to go even further and invite you to meet anywhere in the Ukrainian Donbass, where there is a war going on."
Ukrainian Foreign Minister Dmytro Kuleba has called for new Western economic sanctions to deter Moscow from "further escalation".
Washington and NATO have been alarmed by the large build-up of Russian troops near Ukraine and in Crimea, the peninsula that Moscow annexed from Ukraine in 2014.
Western officials say the concentration of forces is now larger than during that annexation.
The figure given by Mr Kuleba is higher than Ukraine's previous estimate of 80,000 Russian troops, of which 50,000 were new deployments.
He said: "Russian troops continue to arrive in close proximity to our borders in the northeast, in the east and in the south.
"In about a week, they are expected to reach a combined force of over 120,000 troops.
"This does not mean they will stop building up their forces at that number."