Ukrainian President Volodymyr Zelensky on Thursday sought to allay fears over the future of war-ravaged separatist-held territories in the east after protests broke out in Kiev.

More than 1,000 protesters rallied in the centre of the Ukrainian capital on Wednesday after Ukrainian, Russian and separatist negotiators this week agreed on a peace plan for regions held by Kremlin-backed rebels.

The roadmap envisages special status for the territories if they conduct free and fair elections under the Ukrainian constitution.

The announcement sparked anger in Ukraine where broader autonomy for the separatist-held regions remains an explosive issue. A new rally is planned for Sunday.

The ex-Soviet country of 45 million people has gone through two popular uprisings in two decades and is mired in a smouldering conflict with separatists in the industrial east.

The conflict -- the worst East-West crisis since the end of the Cold War -- broke out after Russia annexed Crimea in 2014 and has already claimed some 13,000 lives.

"I respect the constitutional right of every Ukrainian to protest, I hear you and trust me -- I will never betray Ukraine," Zelensky said in a video address to the nation on Thursday.

The 41-year-old president, who came to power in May, implored Ukrainians to keep a cool head and not to "give in to manipulations and provocations of some individuals."

"They really want to use you," he said without being specific.

He said all of society would be involved in drawing up new legislation on the status of the separatist-held territories known locally as Donbass.

"All of us understand that Donbass is Ukraine," he said.

Earlier this week the Ukrainian leader promised that elections in east Ukraine would not take place "at gun point" -- that is before the withdrawal of pro-Russian forces.

Ukrainian President Volodymyr Zelensky and Russian President Vladimir Putin could potentially meet for the first time this month in talks aimed at ending the conflict in eastern Ukraine
Ukrainian President Volodymyr Zelensky and Russian President Vladimir Putin could potentially meet for the first time this month in talks aimed at ending the conflict in eastern Ukraine AFP / Sergei SUPINSKY

Zelensky and Russian President Vladimir Putin could meet for the first time this month in talks aimed at ending the conflict in eastern Ukraine.

The provisional agreement of a plan for the separatist-held regions was a key condition set by Moscow for a meeting.

Such talks would be hosted by French President Emmanuel Macron, who has been spearheading the drive for peace in Ukraine, and would also involve German Chancellor Angela Merkel.

It would be the first such four-way summit since 2016.

'Putin formula'

The roadmap for the separatist-held Donetsk People's Republic and Lugansk People's Republic has been dubbed "the Steinmeier formula", after the former German foreign minister, Frank-Walter Steinmeier, who proposed it.

Some see it as a potential compromise between Kiev and Moscow but Kremlin critics fear the West has tired of Ukraine's long-running crisis and will push Zelensky to make damaging concessions to Russia.

Zelensky's predecessor Petro Poroshenko has called the plan "Putin's formula", claiming it essentially endorses the Russian annexation of Crimea and Moscow's de-facto control of eastern Ukraine.

The US embassy in Kiev said on Thursday it welcomed progress towards peace in eastern Ukraine, adding that Kiev should reinstate control of its borders.

"Free and fair elections require withdrawing Russia-led forces and illegal armed formations from Ukraine's territory," the embassy said in a statement on Twitter.

"Russia needs to display the political will to make this happen".

Kiev and the West have accused Russia of giving military backing to the separatists, which Moscow denies.

Separately, the mission warned US citizens about upcoming rallies in a number of Ukrainian cities.

"Participation in these events are expected to grow through the weekend," the US embassy said.