"We will measure our success, not only by the battles we win, but also by the wars that we end. My proudest legacy will be that of a peacemaker and unifier."

The words of Donald Trump in January's inauguration speech. After lavish praise from many around the world for Gaza's ceasefire deal in Egypt, the U.S. President is now focused on the one battle he has struggled to finish.

The Ukraine conflict still rages after nearly four years, but after 150 minutes on the phone with Russian President Vladimir Putin on Thursday, Trump seems to be in buoyant mood, at least with his rhetoric, and will be confident of finally making peace between Kyiv and Moscow and strutting on the world stage again.

"My whole life, I've made deals," Trump said at the White House late on Thursday. "I think we're going to have this one done, hopefully soon.”

But maybe there's a new sheriff in town, in Budapest anyway, who could be lauded as the world's peacemaker – for bringing the U.S. President and Putin together and creating the stage that stops the bombs and drones from the skies over Kyiv and Moscow.

Viktor Orban, Hungary's Prime Minister, could be that man to steal some of Trump's thunder.

Trump has agreed to a second summit on the Ukraine conflict, proposed to be soon hosted in the Hungarian capital. Orban has had a frantic 24 hours. He spoke with Trump on Thursday and talked to Putin on Friday, saying preparations "are going full steam ahead."

The Kremlin confirmed Putin briefed Orban on his conversation with Trump, but also said there was a great deal to be worked out before a date could be set.

Orban, a long-time Trump ally who has also kept close ties with Moscow, said the meeting could take place within the next two weeks if the U.S. and Russian foreign ministers settled remaining issues at a planned meeting next week.

Orban added: "Budapest is essentially the only place in Europe today where such a meeting could be held, primarily because Hungary is almost the only pro-peace country. For three years, we have been the only country that has consistently, openly, loudly, and actively advocated for peace."

Spotlight on Hungary's capital

The choice of Budapest has raised attention.

The veteran Hungarian premier has often clashed with other EU leaders over Ukraine. Hungary has refused to supply Kyiv with weapons or allow their transfer across its borders since the start of the conflict in February 2022. Orban has threatened to veto certain EU sanctions against Moscow and held up the bloc's adoption of major EU funding packages to Kyiv.

Orban, speaking earlier on Friday on state radio, said the Trump-Putin meeting "will be about peace" and if there is a peace deal, that would lead to a new phase of economic development in Hungary and Europe. He also encouraged Europe to open its own diplomatic channels towards Russia, and again accused the EU of taking what he called a "pro-war stance" over Ukraine.

For now, with the main desire to end the fighting, the European Union is making conciliatory noises. It has welcomed the proposed meeting between Trump and Putin "if it can help bring peace in Ukraine", with a spokesperson emphasizing that Putin was subject to an asset freeze and not a travel ban.

For the record, Putin is facing an arrest warrant from the International Criminal Court, which Hungary is in the process of leaving. Moscow denies the ICC allegations, calling the warrant evidence of the West's hostility to Russia.

There will be many eyebrows being raised in Brussels at the prospect of Orban and Hungary taking center stage for such an occasion. But the concern is likely to be greater in Kyiv, especially for Ukraine President Volodymyr Zelenskyy who is in the White House on Friday, pushing for more military support, including U.S.-made long-range Tomahawk missiles.

Ukraine's relationship with Hungary has become tense. Zelenskyy accused Hungarian drones of crossing into Ukraine last month, prompting Orban to retort that Ukraine was not an independent sovereign state.

Zelenskyy and his country will also be mindful of a certain round of diplomacy in 1994. It was in the Hungarian capital that the U.S., Britain and Russia signed the Budapest Memorandum, providing Ukraine with security assurances in exchange for Kyiv giving up its nuclear weapons. The signatories of that memorandum pledged to respect Ukraine's territorial integrity.

Tomahawk tussle

Trump had seemed in recent days to be increasingly frustrated with Putin and leaning toward granting Zelenskyy fresh support, including the Tomahawk missiles that Ukrainians say would help them push back Russia's momentum on the frontline. 

During Thursday's call, Putin told Trump that supplying long-range missiles to Ukraine would harm the peace process and damage U.S.-Russia ties, a Kremlin aide said. Trump confirmed Putin had opposed such a transfer.

"What do you think he's going to say, 'Please sell Tomahawks?'" Trump joked with reporters. "No, he doesn't want" Tomahawks given to Ukraine, Trump added, calling them a "vicious weapon". Has the U.S. president changed tack again?

Some may argue the threat of long-range missiles landing on Moscow has brought Putin back to the negotiating table. Perhaps Orban deserves some of the praise. 

With a Hungarian election on the horizon, maybe his electorate will think more of their prime minister. It would be good timing for a man whose party trails in the polls.

For now though, the Hungarian leader is playing chief diplomat, regarding himself as the "bridge" between the presidents of the U.S. and Russia. It will be interesting to see how Trump reacts if Orban is the one regarded as the world's top peacemaker.