Merkel's center-left challenger, Martin Schulz, conceded his Social Democrats had suffered a "crushing election defeat," with projections showing the party's worst performance in post-World War II Germany.
He vowed to take his party, the junior partner in Merkel's outgoing "grand coalition" of Germany's traditionally dominant parties, into opposition.
"We have a mandate to form a new government, and no government can be formed against us," Merkel told cheering supporters. She added that it wasn't a "matter of course" to finish first after 12 years in power, and that the past four years were "extremely challenging."
The biggest winner was the four-year-old Alternative for Germany, or AfD. It finished third after a campaign that centered on shrill criticism of Merkel and her decision in 2015 to allow large numbers of migrants into Germany, but also harnessed wider discontent with established politicians.
One of AfD's leaders, Alice Weidel, said it will provide "constructive opposition." But co-leader Alexander Gauland struck a harsher tone, vowing that "we will take our country back" and promising to "chase" Merkel.
Final results released shortly before 4 a.m. (0200 GMT) today showed Merkel's Christian Democratic Union and their Bavaria-only allies, the Christian Social Union, winning 33 per cent of the vote - down from 41.5 per cent four years ago. It was one of their weakest post-war showings.
AfD won 12.6 per cent of the vote. It was followed by the election's other big winner - the pro-business Free Democratic Party, which returned to parliament after a four-year break with 10.7 per cent.
The Free Democrats were Merkel's coalition partners in her second-term government from 2009-2013, but lost all their seats four years ago.
"In a country that is big on schadenfreude, our comeback is an encouraging message - after failure, a new beginning is possible," party leader Christian Lindner told supporters.
All mainstream parties have ruled out working with AfD and Merkel's conservatives won't form a coalition with the Left Party.
That means two politically plausible governments are mathematically feasible: continuing the "grand coalition" or a combination of Merkel's Union bloc, the Free Democrats and Greens.
That alliance is known as a "Jamaica" coalition because the parties' colors match those of the Caribbean nation's flag. It has been tried, with mixed results, in state governments but never in a national government.
"It is completely clear that the role the voters have given us is as the opposition," Schulz said.
Referring to AfD's third-place finish, he said "there cannot be a far-right party leading the opposition in Germany."
Cobbling together a "Jamaica" coalition is likely to be time-consuming. The Free Democrats and Greens are traditional rivals. Four years ago, Merkel's conservatives and the Greens held exploratory talks on a two-party coalition but they came to nothing.
The underwhelming result also looks set to re-ignite pressure within Merkel's bloc for a tougher conservative image. Bavarian Governor Horst Seehofer, who feuded with Merkel over the migrant influx before putting aside their differences this year, said the outcome showed that the conservatives need to close "an open flank to the right."
"We need an answer - there must be no democratic alternative to our right," he added. "As long as it is there, we haven't completely done our homework."
AfD is the first party to the right of the conservatives to enter parliament in 60 years.
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