But Mr Zelensky said it would not be possible to end the almost three years of war in one day, as Mr Trump claimed he could do during his election campaign.
"The 'hot' stage of the war can end quite quickly, if Trump is strong in his position," Mr Zelensky said in a Ukrainian television interview late on Thursday, referring to fighting on the battlefield.
Mr Trump, who takes office on January 20, has not publicly fleshed out his policy on Ukraine but his previous comments have put a question mark over whether the US will continue to be Ukraine's biggest and most important military backer.
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