The 44-year-old leader made the statement while addressing the global media in Kiev on Friday. Speaking to foreign reporters at a press conference on Friday, he said: “I’m the president of Ukraine, I’m based here and I think I know the details deeper than any other president.”
On Thursday, US President Joe Biden said he believed Russia could attack its neighbour next month.
Russia, however, denies it is planning to invade and on Friday its foreign minister said Moscow did not want war.
While Russia has about 100,000 troops on Ukraine’s borders, Mr Zelensky said he did not see a greater threat now than during a similar massing of troops last spring.
He said: “There are signals even from respected leaders of states, they just say that tomorrow there will be war.
“This is panic – how much does it cost for our state?”
The “destabilisation of the situation inside the country” was the biggest threat to Ukraine, he said.
He indirectly criticised the decision by the US to pull family members of diplomats out of the country.
He said: “Diplomats are like captains. They should be the last to leave a sinking ship.
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The White House disputed the read on the call, with National Security Council spokeswoman Emily Horne pushing back on a report that a Ukrainian official said Biden warned Kiev could be “sacked” and to “prepare for impact”.
She tweeted: “This is not true. President Biden said that there is a distinct possibility that the Russians could invade Ukraine in February.
“He has previously said this publicly & we have been warning about this for months.
“Reports of anything more or different than that are completely false.”
She also tweeted out a statement by Ukraine’s US embassy stating “that some reports regarding today’s conversation of President Zelenskyy and President Biden are completely false.
“He also encouraged to carefully treat all information in this troubled time especially from the unconfirmed sources.”