New York City has reached an agreement with animal-advocacy groups under which it will avoid having to build full-time shelters in Queens and the Bronx, but will step up its efforts to sterilize feral cats and to require owners to spay or neuter free-roaming cats.

The program, which is included in legislation that the City Council will vote on this fall, is seen as a way to decrease the unwanted cat population and increase the likelihood that those cats that do enter city shelters will be adopted.

Budget cuts over the past few years have limited the city’s ability to pick up strays, and volunteer organizations have started taking in more cats and dogs that once went to public shelters.

From June 2010 to May 2011, 21,086 cats entered the shelter system, according to the city’s Department of Health and Mental Hygiene, one of the backers of the agreement. Cats accounted for 59 percent of the animals that entered shelters and two-thirds of those that were euthanized.