The European Union signaled on Friday that it was poised to unlock billions of euros in frozen funds for Hungary, a major step toward the thawing of relations with Budapest after the election defeat last month of Viktor Orban, then the prime minister.

Brussels would release 16.4 billion euros (about $19.1 billion) out of more than €19 billion it had withheld to push Mr. Orban’s government into accepting anti-corruption and rule of law policies. His yearslong refusal was at the heart of a re-election strategy that Mr. Orban had used — unsuccessfully — to portray the European Union as bullying Hungary’s economy.

Details about when the money would be released were still being worked out, officials said. But Ursula von der Leyen, the president of the European Commission, sounded confident it would soon be a done deal.

“A new era is beginning for Hungary now,” Ms. von der Leyen told the new Hungarian prime minister, Peter Magyar, after their meeting Friday in Brussels.

“A great deal of work has already been achieved in very short time, and markets are already taking notice, investors’ confidence is returning, trust is being rebuilt,” she said. “This gives confidence for the next steps to come, and we will continue to work together at this pace, each step of our way.”

Mr. Magyar said the money would be used, in part, to protect academic freedoms, build solar and wind farms, buy new trains for a transit system prone to fires, and provide grants to small- and medium-sized businesses to help them with emerging advanced technology.

Mr. Magyar roundly blamed Mr. Orban for failing to strike an agreement on E.U. anti-corruption guidelines that he said he was able to reach in a matter of weeks.

“The previous government could have done it,” Mr. Magyar said, estimating that the €16.4 billion in withheld funding would cover about 13 percent of Hungary’s annual operating budget. “Today, we’ve proven that there was no ideology behind these questions. The only thing that we have to do is to fight corruption.”

He said his government had already taken steps to cement some of the E.U. guidelines, including revising public procurement laws to curb fraud.

A senior European Commission official said that the release of the funds would depend on Hungary completing a series of agreed reforms and investments. The official, who briefed journalists on condition of anonymity, in keeping with standard E.U. practice, said the first payments would likely begin toward the end of this year.

Both Mr. Magyar and Ms. von der Leyen insisted that the agreement to unlock the funds was not linked to whether Hungary would agree to opening talks for Ukraine to join the union, which Mr. Orban had also refused. Ms. von der Leyen said European leaders would discuss that possibility at their next regular meeting, set for June.

Koba Ryckewaert contributed reporting from Brussels.