Lyman lies on the road to the urban centres of Severodonetsk and Kramatorsk.
Russian forces have been closing in on Severodonetsk and nearby Lysychansk in Lugansk province, with conflicting reports about the extent of their advance.
Regional governor Sergiy Gaiday said Russian shelling continued on Severodonetsk as Ukrainian soldiers fought to oust the invading forces from a hotel on its edges, but rejected claims the city had been encircled.
"Severodonetsk has not been cut off... there is still the possibility to deliver humanitarian aid," he told Ukrainian television.
A Lugansk police official, cited by Russia's state news agency RIA Novosti, late Friday said Severodonetsk was "now surrounded" and Ukrainian troops could no longer leave the city.
France, Germany urge talks
Three months after Russia launched its invasion on 24 February, leaving thousands dead on both sides and forcing 6.6 million people out of the country, Moscow has gained control over swathes of eastern and southern Ukraine, including port cities Kherson and Mariupol.
Other Ukrainian ports have been cut off from the world by Russian warships, preventing key grain supplies from being transported out.
Russia and Ukraine supply about 30 per cent of the wheat traded on global markets.
Russia has tightened its own exports and Ukraine has vast amounts stuck in storage, driving up prices and cutting availability for importers across the globe.
President Vladimir Putin has repeatedly rejected any responsibility, instead blaming Western sanctions.
But on Saturday he told French President Emmanuel Macron and German Chancellor Olaf Scholz in a phone call Russia was "ready" to look for ways to allow more wheat onto the global market.
"Russia is ready to help find options for the unhindered export of grain, including the export of Ukrainian grain from the Black Sea ports," the Kremlin reported him as saying.
He called for the lifting of sanctions to allow "an increase in the supply of Russian fertilisers and agricultural products" onto the global market.
Macron and Scholz urged Putin to hold "direct serious negotiations" with Zelensky, the German chancellor's office said.
And they demanded Russia free 2,500 Ukrainian fighters taken as prisoners of war after surrendering earlier this month at a sprawling steelworks in the ravaged port city of Mariupol.
More weapons 'dangerous'
Zelensky late Friday said his country was doing everything to defend the Donbas from intense artillery and missile strikes.
"We are protecting our land in the way that our current defence resources allow. We are doing everything to increase them," he added.
To further help the Ukrainians, Washington was preparing to send advanced long-range rocket systems, US media reports said.
Pentagon spokesman John Kirby did not confirm the plans to deliver the ‘M270 Multiple Launch Rocket System’, highly mobile equipment capable of firing up to 300 kilometres (186 miles) that Kyiv has said it badly needs.
But he said Washington was "still committed to helping them succeed on the battlefield".
British prime minister Boris Johnson pledged his country's continued support "including helping provide the equipment they need" in a call Saturday with Zelensky, his office said.
But Putin warned Macron and Scholz that ramping up arms supplies to Ukraine would be "dangerous" and risk "further destabilisation".
He spoke after his army said it had successfully fired one of its Zircon hypersonic cruise missiles some 1,000 kilometres (625 miles) across the Arctic.
Ship docks in Mariupol
As he seeks to ramp up international pressure on Moscow, Zelensky will speak to EU leaders at an emergency summit Monday as they try to agree on an embargo on Russian oil, which is being held up by Hungary, whose prime minister Viktor Orban has close relations with Putin.
"We need to act until they stop their policy of aggression," Zelensky told a think tank in Indonesia.
But Moscow said Russia expects to receive one trillion rubles ($15 billion) in additional oil and gas revenues this year, a windfall from the sharp rise in oil prices caused in part by its invasion of Ukraine.
In Ukraine, a spokesman for the Russian-controlled Mariupol port said a first ship had docked there on Saturday.
"It will be loaded up with 2.7 tonnes of steel," he told Russian state news agency TASS.
There was however no official announcement from either the Russian or separatist authorities.