Though the city’s Transportation Department has the authority to build bike lanes, Ms. Trottenberg said that her department works closely with community boards and local groups to address their concerns. “We try very hard to get their approval,” she said, adding that they sometimes proceed over objections when there are safety concerns.

She said that 26th and 29th Streets were selected for the new crosstown routes largely because they are wide enough to accommodate protected bike lanes and run continuously across without being cut off by parks or plazas.

Ms. Trottenberg estimated that the cost of each new protected bike lane would be less than $500,000, and would mainly entail redesigning the streets and replacing signs.

Both 26th and 29th Streets have one lane of traffic, and the new bike lanes would take over space that is currently occupied by double-parked vehicles, including trucks making deliveries and taxis picking up and dropping off passengers. Ms. Trottenberg said that more designated loading and unloading areas would be added to those streets.

Last month, the city also announced plans for new crosstown protected bike lanes running in both directions on a 1.5-mile stretch of 13th Street. It will be part of the city’s efforts to provide alternatives to commuters during the planned shutdown of the L train tunnel between Brooklyn and Manhattan in 2019 to repair damage caused by Hurricane Sandy. New protected bike lanes are also planned for several blocks in the East 20s to connect to a new ferry service on the East River, though they would not run all the way across Manhattan.

Paul Steely White, executive director of Transportation Alternatives, an advocacy group, said that protected bike lanes can save lives and the city’s plan “reclaims space that drivers have abused, and turns it into dedicated space for more vulnerable street users.”

Christine Berthet, 66, who lives in Midtown, said that she prefers to do all her riding in protected bike lanes on city streets. “Having a protected bike lane is very comfortable,” she said. “From a safety standpoint, you feel like you don’t have to deal with cars or watch your back.”