The radical leftist party that stormed to a historic victory in January and then governed Greece through a tumultuous seven months won a convincing new mandate in elections on Sunday, giving it another chance to lead a country still mired in economic ruin.

Despite convulsive developments in Greece this year, Syriza’s margin of victory over its nearest rival was almost exactly the same as it was the last time the country voted. The results validated party leader Alexis Tsipras’s decision to take his case to the voters for a third time this year. Syriza has comfortably won each vote.

Party supporters cheered and danced in the streets of downtown Athens on Sunday night after the results became clear and Syriza’s main challenger, the center-right New Democracy party, conceded.

In his victory speech, Tsipras vowed to serve as prime minister for the next four years and promised that Syriza’s win would radiate far beyond Greece’s borders.

“We have a mandate to keep fighting — in this country and outside it,” the 41-year-old told a flag-waving crowd that was conspicuously smaller than after the January vote. “Beginning tomorrow, we start the fight to change Europe.”

By securing first place out of a crowded field that spanned the ideological spectrum from communists to neo-Nazis, Syriza avoided what would have been a stinging rejection by Greek voters and, with it, a likely halt to leftist momentum across Europe.

Instead, leftists continent-wide are likely to be emboldened by the results — particularly in Spain, where a close Syriza ally, Podemos, is challenging the establishment parties in a vote due later this year.

For Syriza, the results give the party a fresh opportunity to steer Greece after an initial stint in power that was marked by erratic decision-making and the near-collapse of the nation’s economy amid a bitter showdown with European creditors.

Tsipras, who became Greece’s youngest prime minister in 150 years when first elected, opted to call a new vote after Syriza split over his July decision to back a deeply controversial $97 billion bailout.

The deal, which came with harsh austerity measures, represented an embarrassing capitulation for a leader who had campaigned as an anti-austerity firebrand and who had only days earlier persuaded voters to reject a similar agreement in a nationwide referendum.

Since then, Tsipras’s popularity has fallen markedly as voters have wondered whether all the brinkmanship was worth it.

Under those circumstances, Sunday’s results were a genuine triumph for Tsipras, said Nick Malkoutzis, editor of the political analysis Web site Macropolis.

But it may be a temporary one.

“He has many battles ahead,” Malkoutzis said. “The first is to form a government. The second is to implement the tough elements of the bailout agreement. And the third is to hold his party together.”

The outlines of a new government became clear late Sunday as Tsipras embraced the leader of the nationalist Independent Greeks party and said they would again team up in a coalition. Together, the two parties have a narrow majority in the new parliament — just as they did in the last — eliminating the need for potentially messy negotiations with other players.

Overall, the results Sunday were remarkably similar to those from the January vote, with Syriza and New Democracy finishing well ahead of the rest of the field. Again, the extreme-right Golden Dawn party appeared headed for a distant third-place finish.

Despite the static results, Malkoutzis said Tsipras must contend with an electorate that is clearly disenchanted, even if it was willing to give him another chance.

“There’s a feeling that voters have run out of options,” Malkoutzis said. “They’ve been exhausted by the last six or seven months, which came on top of an already tiring five or six years.”

Indeed, Sunday’s vote was staged under spectacularly clear, sunny skies that contrasted vividly with the gloomy mood of voters. Many wondered why they were being asked to return to the ballot box for the third time this year, after the January election and the July referendum on the bailout.

Turnout was down significantly from the 64 percent recorded in January. Those who showed up to vote said they were not particularly enthusiastic about the task, noting that all the major parties have already signed off on a bailout deal that will set the country’s course for years with its pension cuts and tax hikes.

“These elections are completely useless. The fate of Greece is already settled,” said Eleni Bagourda, a 45-year-old bookkeeper, adding that she voted Sunday only out of a sense of duty.

As the balloting continued, even Syriza supporters acknowledged that the magic of elections past was gone.

“In January, Syriza raised people’s hopes. Now we’re facing disillusionment,” said Vassilis Sklias, a longtime party member.

But as disappointed as Syriza voters may be by their party’s failure to end austerity, the leftists’ opponents will be even more discouraged by Sunday’s results, which showed no enthusiasm for a return to the establishment-oriented parties that together had governed Greece for decades — until January.

Athanasios Siniosoglou, a 35-year-old cafe owner, said he could not fathom why voters would give Syriza another chance, given the chaos of its aborted fight against Europe.

“They wanted to do something that couldn’t be done,” said Siniosoglou, who backed New Democracy. “The story they were telling was a nice one. But it’s like Texas wanting to fight against America. Can it be done? No.”

Those who wish Syriza had pressed on with its fight also will be chagrined by the election results.

Outspoken former finance minister Yanis Varoufakis threw his weight Sunday behind a splinter faction called Popular Unity, which broke off from Syriza over the bailout. In a typically combative statement, he called Sunday’s vote an attempt to validate “the dead end, humiliating and irrational” bailout.

But his endorsement held little apparent sway: Popular Unity appeared set to fall short of the minimum 3 percent required to win seats in Parliament.

At night’s end, it was Syriza loyalists who were celebrating — and promising that their country would press its fight with European powerbrokers.

“We were disappointed with Europe, not with our leaders,” said Dimitra Anagoustou, a psychiatrist who waved a purple Syriza flag as she awaited Tsipras’s arrival at the victory rally. “The fact is that this is a war. And there will be many more battles.”

Christos Karan contributed to this report.

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