Two Ukrainian soldiers have been killed in clashes with pro-Russia separatists in Ukraine's war-torn east, its military said Monday, as Kiev again accused Moscow of massing tens of thousands of soldiers on its border.

Clashes have regularly broken out in the east in recent weeks, undermining a ceasefire brokered last year that had raised hopes of ending a conflict that erupted in 2014 after Russia annexed Crimea.

The Ukrainian army said that one serviceman was killed on Saturday when separatist fighters opened fire with small arms, while another soldier "received a gunshot bullet wound incompatible with life" on Monday.

The fresh clashes come as Russia has massed thousands of its soldiers on its border with Ukraine, with the White House last week saying the number of Russian troops at the border was now greater than at any time since 2014.

Ukrainian President Volodymyr Zelensky's spokeswoman told AFP on Monday that Russia now has 41,000 troops on Ukraine's eastern border and 42,000 soldiers on the Crimean peninsula.

Spokeswoman Yuliya Mendel also said that Zelensky had sent a query to the Kremlin in late March requesting talks with Russian President Vladimir Putin over the escalating conflict, but was yet to receive an answer.

"We hope that President Vladimir Putin does not refuse dialogue," Mendel told AFP.

Kremlin spokesman Dmitry Peskov, however, denied that Moscow had received a request for talks.

"I am not aware of any such enquiries in recent days," he told reporters on Monday.

The conflict in Ukraine's war-torn east has claimed more than 13,000 lives
The conflict in Ukraine's war-torn east has claimed more than 13,000 lives AFP / STR

Zelensky might also travel to Paris this week to discuss the rising tensions with his French counterpart Emmanuel Macron, an official in the Ukrainian presidency told AFP on condition of anonymity.

Ukraine's former foreign minister Pavlo Klimkin said the significance of such a meeting would be in sending a signal that the European Union stands with Kiev.

"Putin hopes that there will be those in the EU who are afraid of raising the stakes and will try to convince us of the need for a 'compromise'," Klimkin wrote on Facebook.

The Kremlin, which has not denied the troop movements, has said it is not moving towards war with Ukraine, but also that it "will not remain indifferent" to the fate of Russian speakers in the east.

Russian Foreign Minister Sergei Lavrov on Monday warned that the escalating situation "could end badly" because Kiev might "act recklessly".

US Secretary of State Antony Blinken issued his own warning on Sunday, saying there would be "consequences" if Russia acts "aggressively" towards Ukraine.

The conflict, which has claimed more than 13,000 lives, has seen 28 Ukrainian soldiers killed since the start of the year compared to 50 in all of 2020.

Kiev and its Western allies accuse Russia of sending troops and arms to support the separatists, claims Moscow denies.