DETROIT — Detroit reached its first deal with a retired workers group on Tuesday over pension and healthcare benefits and was close to a deal with its two pension funds, giving a major boost to the city’s plan to exit bankruptcy in October.

Momentum for the city’s plan to adjust its $18 billion debt burden was building after Detroit last week won court approval for a crucial settlement over interest rate swaps and reached an agreement with bond insurance companies over the treatment of voter-approved general obligation bonds.

Under the deal with the Retired Detroit Police and Fire Fighters Association announced by U.S. Bankruptcy Court mediators on Tuesday, pensions for retired police and fire workers would not be decreased, but cost-of-living increases would be cut in half. A separate voluntary employee beneficiary association plan or VEBA will be established for retiree healthcare, according to a court statement.

The deal, which is contingent on more than $800 million in contributions for retirees from foundations, the Detroit Institute of Arts and the state of Michigan, marks the first between the bankrupt city and one of its retired worker groups. A deal with pension funds may be close. Tina Bassett, a spokeswoman for Detroit’s General Retirement System, said fund officials “are still negotiating in good faith and hope to be able to announce something soon.”