BERLIN – Chancellor Angela Merkel led her conservatives to a stunning victory in Germany’s election Sunday, a personal triumph that cements her position as Europe’s most powerful leader. However, she will need to reach out to center-left rivals to form a new government after her coalition partner crashed out of Parliament.

Merkel’s Union bloc scored its best result in 23 years to put her on course for a third term, winning 41.5 percent of the vote and finishing only five seats short of an absolute majority in the lower house.

The 59-year-old benefited from a strong economy and low unemployment, which have helped keep her personal popularity sky-high — a contrast with the string of leaders who have lost their jobs in other European countries since the continent’s debt crisis erupted three years ago.

A new coalition probably will not result in any major shifts in German policy, though it could bring a slightly softer tone to managing the crisis.

Merkel, who has been chancellor of Germany since 2005 and is the de facto leader of the European crisis response, which has mixed aid with austerity, told supporters that it was “a super result.”

She did not immediately speculate about the shape of the next government, but made clear she plans to serve a full term.

“I see the next four years in front of me, and I can promise that we will face many tasks at home, in Europe and in the world,” Merkel said during a television appearance with other party leaders.

Despite the scale of her win, governing is not likely to get easier for Merkel.

Her partners of choice, the pro-business Free Democrats, won only 4.8 percent of the vote. The once-influential party fell short of the 5 percent needed to win seats in parliament for the first time in Germany’s post-World War II history, paying the price for frequent coalition infighting and their failure to secure tax cuts that they had pledged to get before going into government four years ago.

Merkel looks likely to end up leading either a “grand coalition” government with the center-left Social Democrats of defeated challenger Peer Steinbrueck — reviving the alliance that ran Germany in her first term — or, less likely, with the environmentalist Greens.

Either way, several weeks of difficult negotiations are expected.

“The ball is in Merkel’s court,” said Steinbrueck, a former finance minister under Merkel who has said he will not serve under her again. “She has to get herself a majority.”

“Angela Merkel is stronger than ever, also in her party,” said Manfred Guellner, the head of the Forsa polling agency. “But governing is going to be odd because she will have to form a ‘grand coalition’ although she is only a few seats away from an absolute majority.”

Merkel’s conservatives finished far ahead of Steinbrueck’s Social Democrats, who won 25.7 percent of the vote — not much better than the postwar low of 23 percent they hit four years ago.Their Green allies polled a disappointing 8.4 percent, while the hard-line Left Party scored 8.6 percent.

But although the three parties on the left together hold a thin parliamentary majority, there is virtually no chance of them governing together. The Left Party includes heirs of East Germany’s former communist rulers, opposes German military deployments abroad and is the only party that voted against Merkel’s policies of bailing out debt-troubled European countries in exchange for reforms. The two center-left parties Sunday renewed promises not to form an alliance with the Left.

“We did not achieve the result we wanted,” Steinbrueck told supporters, insisting he will not engage in “speculation” about the next government.

Merkel’s conservatives, the Social Democrats and Greens “have largely similar positions” on Europe, said Oscar Gabriel, a political science professor at Stuttgart University. He noted, however, that “there are a few nuances,” with the center-left parties more open to limited pooling of European countries’ debt — something the chancellor has refused to countenance.

A “grand coalition” might result in a somewhat greater emphasis on bolstering economic growth over the austerity that Germany has insisted on in exchange for bailing out economically weak European countries such as Greece.

During the election campaign, Merkel and Steinbrueck clashed over center-left calls for tax increases on high earners and a mandatory national minimum wage. Merkel rejected both ideas, arguing that they will hurt the economy.

All the same, a “grand coalition” is more likely to be to put together than a conservative-Green alliance, which would face wider cultural and political differences.

Green leader Juergen Trittin said of possible negotiations: “I don’t think the probability of anything coming out of it is particularly high.”

True to her methodical style, Merkel said Sunday she will proceed “step by step” in working toward a new government.

Still, she beamed earlier in the evening as she was greeted by a cheering crowd chanting, “Angie! Angie! Angie!” at her party’s headquarters.

Merkel pledged that “we will do everything together in the next four years to make them successful years for Germany.”

A new anti-euro party, Alternative for Germany, came close to winning the 5 percent support needed to win seats in Parliament on Sunday. The party, which advocates an “orderly breakup” of the eurozone and appeared to have a wider appeal to protest voters on the right, finished with 4.7 percent.

Its leader, Bernd Lucke, said it had “taught the other parties to be scared” and “strengthened democracy in Germany.”

Merkel has pursued a hard-nosed course during the euro crisis, insisting on spending cuts and economic reforms in exchange for bailout struggling countries such as Greece. The bailouts have not been popular, but Germany has largely escaped the economic fallout from the crisis, and Merkel has won credit for that. Europe played only a very limited role in the campaign.

Still, senior Merkel ally Horst Seehofer, the conservative governor of Bavaria, conceded that the government needs to do a better job of explaining its policies. He told ZDF television he noticed a “communication deficit” on the campaign trail.

There was shocked silence at the Free Democratic Party’s election event as exit polls showed the party slumping below 5 percent of the vote.

Four years ago, the party won nearly 15 percent, its best-ever result. Over the past week, it had pleaded for support from Merkel supporters to keep it afloat. Merkel frequently called the outgoing coalition “the most successful government since reunification” 23 years ago, but her own popularity didn’t extend to the coalition.

“It’s the bitterest, saddest hour of the Free Democratic Party,” said the party’s leader, Vice Chancellor Philipp Roesler.

Gabriel, the political scientist, said conservative voters who voted for the Free Democrats in 2009 “returned in droves” to Merkel. The smaller party, which was long the kingmaker of German politics, “isn’t considered competent by the voters anymore,” he said.

The conservative result was close to an absolute majority because of the rule requiring parties to win 5 percent support to claim seats in the lower house. Many small parties miss that threshold, meaning their votes do not count in the division of seats.

Sunday’s result gives the conservative bloc of Merkel’s Christian Democratic Union and its Bavaria-only sister, the Christian Social Union, 311 seats in Parliament. The Social Democrats won 192 seats, the Greens 63 and the Left Party 64.

Turnout edged up to 71.5 percent from 70.8 percent four years ago.

The euro approached a seven-month high versus the dollar on Monday as markets began reacting to the election.

“This is a vote in favor of Merkel rather than a vote in favor of big changes,” said Steven Englander, Citigroup Inc.’s global head of G-10 currency strategy in New York.

“It’s most likely Merkel will govern in a grand coalition with the Social Democrats,” he added, “so that’s a slight euro positive because the government would be somewhat more friendly to the peripheral nations in the currency bloc.”

The euro rose 0.1 percent to $1.3539 early in London.

European stock markets drifted higher at the start of trading on Monday as dealers digested the outcome of the vote.

London’s benchmark FTSE 100 index firmed 0.05 percent to 6,599.71 points, Frankfurt’s DAX 30 added 0.08 percent to 8,682.94 points and the CAC 40 in Paris rose 0.10 percent to 4,207.99 compared with Friday’s closing levels.