• Oleksii Reznikov said Moscow had amassed thousands of troops and could "try something" to mark the anniversary of the initial invasion last year.
• Meanwhile, three people have died in an attack on the city of Kramatorsk.
Ukraine's defence minister has said Russia is preparing a major new offensive, and warned that it could begin as soon as 24 February.
Oleksii Reznikov said Moscow had amassed thousands of troops and could "try something" to mark the anniversary of the initial invasion last year.
The attack would also mark Russia's Defender of the Fatherland Day on 23 February, which celebrates the army.
Meanwhile, three people have died in an attack on the city of Kramatorsk.
Seven others were wounded in the city in Donetsk region after a Russian missile struck a residential building, the provincial governor said.
The toll is expected to rise as rescuers comb through the wreckage.
"The only way to stop Russian terrorism is to defeat it," Mr Zelensky wrote on social media about the attack. "By tanks. Fighter jets. Long-range missiles."
Ukraine has recently renewed calls for fighter jets to help protect itself from air attacks after Germany, the US and the UK agreed to send them tanks.
Mr Reznikov said Moscow had mobilised some 500,000 troops for the potential offensive.
In September, Russian President Vladimir Putin announced a general mobilisation of some 300,000 conscripted troops, which he said was necessary to ensure the country's "territorial integrity".
But Mr Reznikov suggested that the true figure recruited and deployed to Ukraine could be far higher.
"Officially they announced 300,000 but when we see the troops at the borders, according to our assessments it is much more," he told the French BFM network. The BBC cannot independently verify this figure.
Despite some heavy fighting in the eastern Donbas region, the war has entered something of a stalemate in recent months since Ukraine retook the southern city of Kherson.
With the exception of the Russian seizure of the town of Soledar, neither side has made major territorial advances.
But a Russian spring offensive - and a Ukrainian counter-offensive - has long been considered likely. The US-based Institute for the Study of War (ISW) recently said that Moscow could seek to "undertake a decisive action" and launch a "big offensive" in the east.
Mr Reznikov said Ukraine's commanders would seek to "stabilise the front and prepare for a counter-offensive" ahead of the rumoured Russian advance.
"I have faith that the year 2023 can be the year of military victory," he said, adding that Ukraine's forces "cannot lose the initiative" they have achieved in recent months.
The defence minister was in France to strike a deal to purchase additional MG-200 air defence radars, which he said would "significantly increase the capacity of the armed forces to detect air targets, including winged and ballistic missiles, and drones of various types".
Mr Reznikov's comments come as Ukrainian intelligence alleges that President Putin has ordered his forces to seize the Donbas before the end of spring.
But speaking on Monday, Nato Secretary-General Jens Stoltenberg warned that there were no indications that Mr Putin had limited his military goals to seizing eastern regions of Ukraine.
"That they are actively acquiring new weapons, more ammunition, ramping up their own production, but also acquiring more weapons from other authoritarian states like Iran and North Korea," Mr Stoltenberg said.
"And most of all, we have seen no sign that President Putin has changed his overall goal of this invasion - that is to control a neighbour, to control Ukraine. So as long as this is the case, we need to be prepared for the long haul."
Meanwhile, Ukraine's Deputy Defence Minister Hanna Malyar said that intense fighting was continuing in the Donbas region, where Russian forces and Wagner Group mercenaries have been trying to take the town of Bakhmut.
She added that Moscow's troops were also trying to seize Lyman - the former Russian logistics hub that Ukrainian troops retook in October.
"Russian troops are actively trying to reach the borders of Donetsk and Luhansk regions," she wrote on the Telegram messaging app. "Our soldiers defend every centimetre of Ukrainian land," she said.
Speaking on Wednesday night, Mr Zelensky warned that the situation on the front lines of the conflict was testing his forces.
"There is a certain increase in the occupiers' offensive actions at the front - in the east of our country, Mr Zelensky said. "The situation is becoming even more severe."
While the Wagner group has claimed it has been heavily involved in Russia's recent advances in the east, a former commander who fled to Norway has told Reuters that he witnessed the killing and mistreatment of Russian prisoners taken to Ukraine to fight for the group.
Andrei Medvedev made an unverified claim that in the four months he was with Wagner, he saw two people who didn't want to fight being shot.
About 80% of Wagner's personnel in Ukraine have been drawn from prisons, according to the US National Security Council.