"At the end of the Hungarian presidency in the EU, we made new efforts for peace. We proposed a ceasefire during Christmas and a large-scale prisoner exchange", writes Orbán on X and adds that it is "sad" that Zelenskyj "clearly rejected and excluded" the proposals.
Ukraine says that the issue was never raised.
"As usual, the Hungarian side discussed nothing with Ukraine. As usual, the Hungarian side did not warn us about the contacts with Moscow", says the president's adviser Dmytro Lytvyn in a written statement.
Orbán spoke earlier on Wednesday by phone with Russia's President Vladimir Putin, and the Kremlin describes the conversation as "a thorough exchange of views on Ukrainian issues".
Putin is said to have stated that Ukraine has taken a "destructive" stance that excludes a peace agreement.
According to the Kremlin, the conversation was held at Hungary's request and Orbán expressed interest in helping to find "political-diplomatic ways to resolve the crisis".
Ukraine's President Volodymyr Zelenskyj criticizes Orbán after the conversation.
"No one should strengthen their personal image at the expense of unity: everyone should focus on common success. Unity in Europe has always been the key to achieving this", he writes on X.
