CHICAGO — After a tougher-than-expected re-election, Chicago Mayor Rahm Emanuel is pledging to take a new approach as he faces rising pension costs, ongoing gang violence and negotiations with labor unions that spent millions trying to defeat him.

Emanuel, a former congressman and chief of staff to President Barack Obama, won a second term Tuesday over a lesser-known opponent, Cook County Commissioner Jesus “Chuy” Garcia. Though he led Garcia by about 11 points with nearly all precincts reporting, the victory came only after Emanuel failed to win a majority in a first-round February contest, forcing him and Garcia into Chicago’s first runoff mayoral election.

In a victory speech, he said he understands the challenges facing Chicago will require him to lead “in a different fashion,” a nod to a management style he’s acknowledged has rubbed some voters the wrong way.

“In the era of hard choices, I can’t promise that everyone will be pleased with every decision,” he told a room of cheering supporters gathered at a union hall. “But the challenges we face, we face together as one community, one city, one voice where every voice counts.”

Emanuel campaigned hard to persuade voters he was the better choice to lead the nation’s third-largest city through a raft of crises. He also defended his Democratic credentials as Garcia and progressive groups accused him of putting Chicago’s corporate interests ahead of the working people who make up the city’s neighborhoods.

He performed better across the city during the runoff than he did six weeks earlier, when two of the four challengers were black. During the February election, Emanuel’s support fell in predominantly African-American areas compared with 2011, when he won a first term.

The exception Tuesday was in Chicago’s heaviest Hispanic wards, where Garcia, a Mexican immigrant, saw his strongest support.

Bruce Puffer, a 56-year-old bartender, voted for Garcia, saying Chicago needs “a regular guy” running the city. But he said it will be tough going, regardless of who is mayor.

“Nobody wants to say it, but there are going to have to be budget cuts, service cuts and the worst thing looming is that pension cuts are going to have to be made. That’s the elephant in the room,” Puffer said. “People promise too many things, and they can’t deliver on them.”

While Emanuel enjoyed strong support from trade unions that benefit from big construction projects and other development, Garcia had the backing of teachers unions, which spent more than $1 million and provided many of the foot soldiers Garcia’s campaign used to get voters to the polls.

Emanuel’s administration now must negotiate a new contract with the Chicago Teachers Union.

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