SAN JOSE — A controversial project that replaces hundreds of affordable homes with denser market-rate apartments will move forward, city leaders decided this week, despite sharp objections from housing advocates and soon-to-be displaced renters.

The City Council voted 7-3 during a marathon meeting Tuesday to deny an appeal from tenants who say they’ll become homeless if the development is approved. Council members Ash Kalra, Tam Nguyen and Magdalena Carrasco were opposed. Vice Mayor Rose Herrera was absent.

The project’s developer, Greystar Real Estate Partners, proposes tearing down the 216-unit Reserve apartment complex on South Winchester Boulevard and building 640 new apartments in a cluster of four- or five-story buildings.

The units would sit on top of 8,000 square feet of retail space with a decorative public plaza and outdoor dining options. A two-level basement garage would be built to hold 960 cars.

While most agree San Jose desperately needs more housing, the project means losing 216 apartments under rent control, a policy that prevents landlords from raising rents beyond 5 percent a year. Those rent-controlled Reserve units won’t be replaced anywhere else in the city.

A group of displaced residents, who say they can’t afford higher rents elsewhere, banded together to fight the city’s approval of Greystar’s permits and environmental clearance. But they lost that battle Tuesday when the council majority denied the appeal and sided with city planning officials who said the project meets all requirements.

“This is a blow to us,” said Brandie Locke, 30, a longtime Reserve resident who pays $2,200 for a one-bedroom apartment. “It’s very stressful. It costs a lot to move and we can’t start a family. We wake up every day wondering where we will go.”

Councilman Chappie Jones, whose district includes the project, acknowledged the consequences of the new development but said increasing San Jose’s housing stock is the only way to stabilize skyrocketing rents. That’s why he supports the project.

“The city has to build enough housing to meet the demand,” Jones said. “We have to build high density in these strategic locations, and that’s why this was a decision I had to make.”

Jones pushed the developer to offer Reserve residents some relocation benefits. He’s also asking the city to adopt an ordinance to make that a requirement for future development that displaces renters.

Greystar agreed to paying tenants three months of market-rate rent. Residents who are disabled, elderly or have more than one dependent child would receive an extra $3,000 to help them move out. But only 40 units will qualify for the benefits based on their income, though the company plans to offer it immediately.

Kalra, one of the dissenters Tuesday, said the city should have delayed approving the project until it figures out how to help residents find other housing. He said the city has a “moral obligation” to do everything it can.

“You’re talking about over 600 residents who will be displaced,” Kalra said. “I’m not going to cry tears for residential developers in the valley right now who are making a fortune. I think we have a greater obligation to our residents.”

Contact Ramona Giwargis at 408-920-5705. Follow her at Twitter.com/ramonagiwargis.