WARSAW, Poland — The majority of voters in Poland’s general election supported opposition parties who promised to repair the nation’s constitutional order and its relationship with allies, including the European Union and Ukraine, according to projections Monday.

After a bitter and emotional campaign, voters turned out in droves on Sunday to make their voice known. Turnout was at the highest level in the country’s 34 years of democracy, surpassing the 63% who turned out in the historic 1989 vote that toppled communism.

The final result was not expected for many hours. But a so-called late exit poll by Ipsos suggested that voters had finally grown tired of the ruling nationalist party, Law and Justice, after eight years of divisive policies that led to frequent street protests, bitter divisions even within families and billions of euros in funding held up by the EU over rule of law violations.

The poll showed that three centrist opposition parties that campaigned on a promise to reverse the illiberal drift of the government had together secured around 248 seats in the 460-seat lower house of parliament, or Sejm — a clear majority.

“I am really overjoyed now,” Magdalena Chmieluk, a 43-year-old accountant, said on Monday morning. The opposition “will form a government and we will finally be able to live in a normal country, for real.”

Still, Poles on Monday were facing weeks of political uncertainty. Law and Justice won more votes than any single party and said it would try to keep governing.

“No matter how you look at it, we won,” Law and Justice campaign manager Joachim Brudzinski said Monday morning in an interview on the RMF FM radio broadcaster.

He said that his party would try to build a government led by Prime Minister Mateusz Morawiecki.

President Andrzej Duda, an ally of Law and Justice, must call the first session of the new parliament within 30 days of the election and designate a prime minister to try to build a government. In the meantime, the current government will remain in a caretaker role.

The tradition in the democratic era has been for the president to first tap someone from the party with the most votes, but he is not required to do so.

It was not clear how Law and Justice could realistically hold onto power, unless it managed to win over some lawmakers from opposition parties, something it did in the past to maintain the thin parliamentary majority it held for eight years. But that seemed unlikely given the large number it would be required to change allegiances.

The Ipsos poll showed Law and Justice with 36.6% of the votes cast; the opposition Civic Coalition, led by former European Council President Donald Tusk, with 31%; the centrist Third Way coalition with 13.5%; the Left party with 8.6%; and the far-right Confederation with 6.4%.

The electoral commission said it expected to report the final result by early Tuesday.

Tusk on Sunday evening declared that it was the end of Law and Justice rule and that a new era had begun for Poland.

Some Polish media were more cautious on Monday, only reporting that the opposition could take power.

Cezary Tomczyk, vice-chairman of Tusk’s party, said the governing party would do everything to try to maintain power. He called on it to accept the election result, saying it was the will of the people to hand over power to the opposition.

“The nation spoke,” Tomczyk said.