By Matthew Dolan and Andrea Gallo 

Leaders of Detroit pension funds expressed relief Tuesday after voting results showed pension holders endorsed the Motor City's historic reorganization plan, but bond insurers voiced continued opposition, signaling a bumpy road ahead in bankruptcy court.

"Most of the retirees are looking forward to an income to have a little certainty in their life. We're just glad it's over," said Don Taylor, president of the Retired Detroit Police and Firefighters Association.

General retirees, who comprise the bulk of those affected, would have their pensions cut by 4.5% and would lose cost-of-living increases. Retired police officers and firefighters would surrender part of their annual cost-of-living increases.

But the approval drew criticism from bond insurers, who remain opposed to the plan of reorganization.

"We understand why the retirees and unions voted in favor of the city's plan--if we were offered a similar deal we too would approve the plan," said bond insurer Financial Guarantee Insurance Co. "Unfortunately, the city's current offer to FGIC and [certain] bondholders in the plan is completely inferior, and until the city treats us fairly, we are compelled to fight for the fair and equitable treatment that is our right under the bankruptcy code."

Contingent on the vote was an agreement by the state and private donors to make $816 million available to shore up pensions. That amount represents the present value of the city's world-class Detroit Institute of Arts collection, which the city said would be placed in a separate trust. The fundraising effort, dubbed the "grand bargain" locally, is meant to allow the city to extract value from the collection to pay down debt while keeping one of the Motor City's cultural crown jewels intact and available to the public.

"We are not surprised at the vote, given the grand bargain's illegal diversion of highly valuable assets to the very creditors who voted yes, " James Sprayregen, an attorney for bond insurer Syncora Guarantee Inc., said in a statement Tuesday, according to the Associated Press. "We look forward to...demonstrating to the court that the plan cannot legally be confirmed given its unfair discrimination against financial creditors and other serious infirmities."

The vote, after weeks of tense campaigning, sets up a confirmation trial scheduled for next month on the city's restructuring plan, the final phase of the bankruptcy case.

Federal bankruptcy judge Steven Rhodes will have the final say, and will hold a trial on whether the reorganization plan, which also includes about $1.5 billion in reinvestment in services and blight removal, is viable. The judge will also likely address the criticism by some bond insurers that pension holders have been treated too well compared with other creditors.

The official count, filed late Monday night, showed 82% of voters eligible for a police or fire pension supported the plan. Roughly 73% of other retirees and employees with pension benefits who voted favored the plan. Voting ran from May to early July.

The pension holders' voting margins were seen as an endorsement of the city's plan to confront an estimated $18 billion in long-term obligations.

"The voting shows strong support for the city's plan to adjust its debts and for the investment necessary to provide essential services and put Detroit on secure financial footing," Detroit Emergency Manager Kevyn Orr said.

On Monday, a court-appointed, independent financial expert found the city would likely be able to provide basic municipal services, meet revised obligations to creditors and avoid future default under the plan's terms and using its assumptions.

"There's still a lot more work to be done. It isn't over until the fat lady sings," said Tina Bassett, spokeswoman for Detroit's General Retirement Pension System.

Write to Matthew Dolan at matthew.dolan@wsj.com