BUDAPEST — The meeting of Prime Minister Viktor Orbán of Hungary with President Putin at Moscow for what he describes as a “peace mission” comes amid growing questions over President Trump’s purported plan to end the Ukraine War if he is re-elected.

Mr. Orbán’s visit comes only days after he made a similar unannounced trip to Ukraine, where he met with President Zelensky and proposed that Ukraine consider agreeing to an immediate cease-fire with Russia.

The Hungarian premier’s attempt at shuttle diplomacy follows the question of how to end the war in Ukraine rising in America’s presidential contest.

During the June 27 debate between Presidents Trump and Biden, Trump observed that he would be able to quickly end the war in Ukraine if he wins re-election, without specifying details.

That comment appeared to pique Mr. Putin’s interest. The Russian leader noted that “the fact that Mr. Trump, as a presidential candidate, declares that he is ready and wants to stop the war in Ukraine, we take this completely seriously.” Mr. Putin cautioned that “I am not, of course, familiar with possible proposals for how he plans to do this.”

President Zelensky for his part urged Trump to disclose his plan to end the war, but warned Ukraine would not accept terms that infringed on the invaded nation’s independence.

“If Trump knows how to finish this war, he should tell us today,” Mr. Zelensky told Bloomberg Television on Wednesday. “If there are risks to Ukrainian independence, if we lose statehood – we want to be ready for this, we want to know.”

Mr. Putin’s own recent proffer of a cease-fire in Ukraine was dismissed by European leaders including Prime Minister Giorgia Meloni of Italy, who denounced the suggestion as “propaganda” that implied Ukraine “must withdraw from Ukraine.”

Mr. Orban’s trip to Moscow marks a rare visit to Russia by a European leader since it invaded Ukraine more than two years ago.

The Hungarian prime minister, widely seen as having the warmest relations with Vladimir Putin among all European Union leaders, has routinely blocked, delayed or watered down EU efforts to assist Ukraine and impose sanctions on Moscow for its war.

He has long argued for a cessation of hostilities in Ukraine but without outlining what that might mean for the country’s territorial integrity or future security.

That posture has frustrated Hungary’s EU and NATO allies, which have broadly considered Russia’s invasion as a breach of international law and a threat to the security of countries in Eastern Europe.

The Hungarian leader’s trip comes “as part of his peace mission,” his press chief, Bertalan Havasi, says, reflecting the image of a peacemaker that the populist leader has cultivated since Russia began its full-scale invasion in February 2022.

Hungary’s foreign minister, Péter Szijjártó, also joined the trip to Moscow, according to a post on his Facebook page.

Hungary at the beginning of the month took over the six-month rotating presidency of the EU Council, a largely formal role that can be used to shape the bloc’s policy agenda. Mr. Orbán has said he wants to use the presidency to advocate for an end to the fighting in Ukraine.

Kremlin spokesman Dmitry Peskov confirmed to a Russian state TV reporter on Friday that Ukraine will be among the topics on the agenda when Mr. Orbán and Putin meet.

EU officials have come down hard on Mr. Orbán for his visit with Mr. Putin, something only one other European leader has done since the start of the invasion.

The bloc’s foreign policy chief, Josep Borrell, said in a statement that Orbán’s visit to Moscow “takes place, exclusively, in the framework of the bilateral relations between Hungary and Russia.”

“Prime Minister Orbán has not received any mandate from the EU Council to visit Moscow. The EU position on Russia’s war of aggression against Ukraine is reflected in many European Council conclusions,” Mr. Borell said.

“That position excludes official contacts between the EU and President Putin. The Hungarian Prime Minister is thus not representing the EU in any form,” Mr. Borrell added.

He added that Mr. Putin has been indicted by the International Criminal Court and an arrest warrant released for his role in relation to the forced deportation of children from Ukraine to Russia.

Speaking to Hungarian state radio before departing Friday morning, Mr. Orbán said he was aware that his country’s presidency of the EU “does not entitle us to negotiate on behalf of anyone.”