BRUSSELS—Ukrainian President Volodymyr Zelensky, having failed to secure new commitments for weapons from the U.S. this week, shifts his attention to Europe, where a fight is deepening over how to keep Ukraine’s government running during its war with Russia.

       While less visible than guns and ammunition, the aid is no less vital for Ukraine’s survival. The European Union has provided Kyiv with billions of euros in crucial funding that has allowed it to keep hospitals, schools and power plants running, pay veterans’ benefits and rebuild homes.

       A four-year budget package valued at more than $54 billion will be at the center of disputes when EU leaders gather today for a scheduled summit amid acrimony over the bloc’s approach to Ukraine.

       Not long ago, the gathering was envisioned as a chance for the EU to cement its long-term commitment to Ukraine in its struggle against Russia, by not only agreeing on a multiyear financial-aid package but also formally inviting Kyiv to start negotiations toward becoming a member of the 27-country bloc. Both those objectives are now in doubt, as are prospects for other steps to help Ukraine, such as a new round of sanctions on Russia.

       Zelensky is expected to speak to the leaders Thursday to make his case, either by video link or on a short trip to the EU capital to join the summit. In Oslo on Wednesday, Zelensky said that an EU rejection of new outreach to Ukraine, particularly launching membership talks, would advance Russian President Vladimir Putin’s aims.

       “If there isn’t a positive decision, it will mean that Putin has vetoed the decision," Zelensky said.

       European disagreements, which echo similar infighting in Washington, are raising questions about the durability of Western commitments to Ukraine. Leaders of countries in the North Atlantic Treaty Organization have said since Russia’s invasion of Ukraine early last year that they would support Kyiv for as long as necessary for it to prevail, and do so on Ukrainian terms.

       But Ukrainian forces are now depleting dwindling quantities of ammunition, equipment and other crucial supplies, while the government’s financial outlook grows uncertain. The doubts over European and U.S. aid are undercutting the message Western capitals have long insisted they need to send to the Kremlin: that they would continue backing Ukraine indefinitely, so Putin should seek peace now.

       “As the war drags on we must prove what it means to support Ukraine for as long as it takes," European Commission President Ursula von der Leyen said Wednesday.

       She said Ukraine needs stable financing over the coming years “so that it can be stronger tomorrow at the table, when it is negotiating a long-lasting and just peace for Ukraine."

       At the center of the fight is Hungarian Prime Minister Viktor Orban, who has repeatedly opposed EU proposals regarding Ukraine. He maintains a cordial relationship with Putin, opposes Western sanctions on Moscow, has blocked Western military support for Ukraine and criticized Ukraine—all of which have repeatedly stretched EU unity to a breaking point.

       Ukraine’s expected budget deficit for 2024 is around $43 billion, and foreign assistance is crucial to covering that gap as the war has devastated its economy. The EU has so far been covering more than half of Ukraine’s annual budget gap during the war, including more than $19 billion, or €18 billion, in financial assistance this year. The four-year package is designed to give Ukraine and potential investors confidence that the country can stave off bankruptcy in coming years.

       European officials had tried to keep the infighting behind closed doors, and French President Emmanuel Macron hosted Orban in Paris last week, seeking compromise. But tensions broke open after what Zelensky called a “frank" discussion with Orban at the inauguration of Argentina’s new president in Buenos Aires on Sunday, which was captured on video but without audible sound.

       “I wouldn’t call it a negotiating situation, but he had something to say to me, and so we took the opportunity to exchange words," Orban said in a podcast Wednesday.

       “The only way I can read the Hungarian position…is that they are against Europe and everything it stands for," said Gabrielius Landsbergis, the foreign minister of Lithuania, one of Ukraine’s strongest backers.

       To assuage Hungary’s block on accession talks, Ukraine’s government has pushed through Parliament several pieces of legislation sought by Brussels, including a law designed to protect education and language rights for minorities. Ukraine has a significant Hungarian minority. The law was among topics Zelensky discussed with Orban in Argentina, Orban said.

       The new law “must remove the concern consistently expressed by Hungary" about starting membership talks, Ukrainian Foreign Minister Dmytro Kuleba said this week.

       Orban, despite supporting the EU decision to make Ukraine a candidate country for EU membership last year, has in recent weeks said the decision runs against Hungary’s national interests.

       He isn’t the only one wary of enlargement. European diplomats say other member states, including Slovakia and Austria, have expressed concerns. Orban, though, is the only leader prepared to veto the start of accession talks, they say.

       On the financial package, Orban argues that the Western strategy for supporting Ukraine hasn’t worked on the battlefield and that allies should be throwing resources behind a peace push despite a 40% planned increase in Russian military spending on the war next year. He has repeatedly said Ukraine is corrupt.

       Hovering over the Ukraine discussions is an issue on which Orban has long been focused: roughly €30 billion in EU budget and pandemic-recovery funding that Brussels has withheld from his government over what the EU says are breaches of its rules on judicial independence, corruption and budget management.

       EU officials unblocked around €10 billion of those funds on Wednesday and more could follow in the new year. Hungarian officials hinted this week that if all the EU money is released, they might consider some kind of financial package for Ukraine.

       However, the EU could give some money to Ukraine bypassing Hungary if the other 26 member states agree. That would likely give Kyiv a financial lifeline at least through 2024.

       Write to Laurence Norman at laurence.norman@wsj.com and Daniel Michaels at Dan.Michaels@wsj.com