Russian-backed separatist rebels and Ukrainian troops have been clashing in the east of the country.
Russia has also been building up troops on the border with Ukraine.
The official, Dmitry Kozak, said that Russian forces could intervene to “defend” its citizens.
“Everything depends on the scale of the conflagration,” he said.
He also warned that an escalation could mark the “beginning of the end” for Ukraine – “not a shot in the leg, but in the face”.
The United States and Germany have both expressed concern at the increase in tensions.
Why are tensions rising between Ukraine and Russia?
Russia has been increasing the number of troops at the Ukrainian border, but at the same time maintains that they should not be seen as a threat.
White House press secretary Jen Psaki said Russian troop numbers there were the highest since 2014, when the conflict in eastern Ukraine began. She described the situation as “deeply concerning”.
Russia has not detailed troop numbers, but the Ukrainian military asserted at the end of March that some 20,000 Russian troops had been moved towards Ukraine’s border. Video has emerged on social media of Russian trains moving heavy weaponry towards the region.
Clashes between Ukrainian troops and the Moscow-backed rebels inside Donbass have also increased in recent months.
Peace deal explained
The death of another Ukrainian soldier on Thursday brought the number killed this year to 25. Fifty Ukrainian troops died in the whole of last year.
For their part, the rebels said one of their fighters was killed on the same day when Ukrainian troops fired 14 mortar bombs at a village on the outskirts of the city of Donetsk.
Map of eastern Ukraine
In a further sign of the seriousness of the situation, Ukrainian President Volodymyr Zelensky visited the region on Thursday to see “the locations of the escalation” and “be with our soldiers in the tough times in Donbass”.
Chancellor Merkel spoke to Mr Putin on the phone on Thursday and called on Russia to “de-escalate tensions” by reducing its troop reinforcements.
In the same call, Mr Putin accused Ukraine of inflaming the situation in the east.
What else did the Kremlin official say?
In Moscow, Mr Kozak likened the current situation of the separatists to Srebrenica, the town in Bosnia-Hercegovina where 8,000 Muslim men were killed by Bosnian Serb forces in 1995.
“If, as our president says, there is a Srebrenica there, we shall probably have to come to their defence,” Mr Kozak said. He is the deputy head of Russia’s presidential administration.
Map of eastern Ukraine
Russian President Vladimir Putin first suggested in 2019 that Russian-speaking residents might suffer a Srebrenica-like massacre if Ukraine regained full control of Donbass without guarantees.
But there have been no reports of any such atrocity being planned.
Mr Kozak suggested the rebels could hold their own for now against Ukrainian forces as they consisted of “battle-hardened units”.
What’s the background to all this?
The roots of the current conflict go back to March 2014 when Russia annexed the Ukrainian region of Crimea.
This sparked a major rift with Western nations, prompting the European Union and the US to impose sanctions on Russia.
A month later, Russian-backed rebels in the predominantly Russian-speaking Donbass seized the Donetsk and Luhansk regions.
media captionCarl Bildt: We don’t know where this will lead us
Western countries and Nato accused Russia of sending troops over the border into Ukraine, but Russia maintains any Russian fighters there are “volunteers”.
Ukraine’s President Zelenskiy came to power promising to bring about peace, and a ceasefire was signed last July. Both sides have since accused each other of violating it.