Yet the city’s plan goes further than many others, its proponents say, by expanding the categories of professionals authorized to vouch for a patient’s gender transition, and by refocusing their expertise away from medical or therapeutic processes and onto a person’s conception of him or herself.

The longstanding requirement of convertive surgery would be abandoned under the proposal, and old birth records, including all supporting documentation, would be sealed, according to Mr. Johnson’s office.

Though an expansion of transgender rights has not been considered a signature issue for Mayor Bill de Blasio, he did express support as a candidate for easing the requirements in changing the gender designation on birth certificates.

And in July, when the mayor signed legislation to create a new municipal identification card, he noted that transgender people would for the first time be allowed to choose the gender designation on their IDs.

“That’s an important opportunity,” he said.

The measure, which would need to pass the City Council to become law, is supported by its speaker, Melissa Mark-Viverito. On Tuesday, the city’s Board of Health introduced an equivalent set of guidelines, supported by the health commissioner, Dr. Mary T. Bassett. The changes could come to a board vote in December.

By pursuing the policy on parallel tracks, the city could preempt any legal concerns about whether the administration or the Council has the authority to approve the shift. (Court decisions last year invalidating Mayor Michael R. Bloomberg’s proposed ban on large sugary drinks called into question the board’s ability to enact changes on its own.)

New York City is one of 57 jurisdictions in the country, including New York State, that have responsibility for their own birth registration, according to the city’s Department of Health and Mental Hygiene.