Some right-leaning parties said the results vindicated their reluctance to spend more on company bailouts and fiscal stimulus amid the global economic crisis.
First projections by the European Union showed center-right parties would have the most seats — between 263 and 273 — in the 736-member parliament. Center-left parties were expected to get between 155 to 165 seats.
Right-leaning governments were ahead of the opposition in Germany, France, Italy and Belgium, while conservative opposition parties were leading in Britain and Spain.
Greece was the exception, where the governing conservatives were headed for defeat in the wake of corruption scandals and economic woes.
Germany's Social Democrats headed to their worst showing in a nationwide election since World War II. Four months before Germany holds its own national election, the outcome boosted conservative Chancellor Angela Merkel's hopes of ending the tense left-right "grand coalition" that has led the European Union's most populous nation since 2005.
"We are the force that is acting level-headedly and correctly in this financial and economic crisis," said Volker Kauder, the leader of Merkel's party in the German parliament.
France's Interior Ministry said partial results showed the governing conservatives in the lead, with the Socialists in a distant second and the Europe Ecologie environmentalist party a close third.
French Socialists said their defeat signaled a need to rethink left-wing policies if they are to have any hope of unseating President Nicolas Sarkozy.
An EU estimate showed that only 43 percent of 375 million eligible voters cast ballots in European parliament elections, a record low amid widespread disenchantment with the continentwide legislature.
The EU parliament has evolved over five decades from a consultative legislature to one with the power to vote on or amend two-thirds of all EU laws. Lawmakers get five-year terms and residents vote for lawmakers from their own countries.
Britain, Ireland, the Netherlands and five other EU nations cast ballots over the last three days, while the rest of the 27-nation bloc voted Sunday.
"Tonight is a very difficult evening for Socialists in many nations in Europe," Martin Schulz, the leader of the Socialists in the European Parliament, told party faithful in Brussels via video link from Berlin. "(We will) continue to fight for social democracy in Europe."
Many Socialists ran campaigns that slammed center-right leaders for failing to rein in financial markets and spend enough to stimulate faltering economies.
Graham Watson, leader of the EU's center-right Liberal Democrat grouping, said early results suggested a rejection of the Socialist approach.
"People don't want a return to socialism and that's why the majority here will be a center-right majority," he said.
In Spain, the conservative Popular Party won two more seats than the ruling Socialists — 23 to 21 seats — with over 88 percent of the vote counted.
Exit polls also showed gains for far-right groups and other fringe parties due to record low turnout.
Near-final results showed Austria's main rightist party gaining strongly while the ruling Social Democrats lost substantial ground. The big winner in Austria was the rightist Freedom Party, which more than doubled its strength over the 2004 elections to 13.1 percent of the vote. It campaigned on an anti-Islam platform.
In the Netherlands, Geert Wilders' anti-Islamic party took 17 percent of the country's votes, taking four of 25 seats.
The Hungarian far-right Jobbik party won three of 22 seats, with the main center-right opposition party, Fidesz, capturing 14 seats and the governing Socialists only four.
Jobbik describes itself as Euro-skeptic and anti-immigration and wants police to crack down on petty crimes committed by Gypsies. Critics say the party is racist and anti-Semitic.
Fringe groups could use the EU parliament as a platform for their extreme views but were not expected to affect the assembly's increasingly influential lawmaking on issues ranging from climate change to cell-phone roaming charges.
The parliament can also amend the EU budget — euro120 billion ($170 billion) this year — and approves candidates for the European Commission, the EU administration and the board of the European Central Bank.
Italian Premier Silvio Berlusconi's Freedom People's Party held a two-digit lead over his main center-left rival in the most recent polling despite a deep recession and a scandal over allegations he had an inappropriate relationship with a young model. Italian results were being released Monday.
In Britain, dissident Labour legislators said a plot to oust Prime Minister Gordon Brown could accelerate after the party's expected dismal results in the European elections were announced.
Brown has been struggling with the economic crisis and a scandal over lawmakers' expenses, and the opposition Conservatives are expected to win the next national election, which must be called by June 2010.
An exit poll in Sweden showed the Pirate Party, which advocates shortening the duration of copyright protection and allowing noncommercial file-sharing, capturing 7.4 percent of the vote.