WASHINGTON — Tenants in nearly a million apartments subject to New York City’s rent regulations could breathe a sigh of relief on Monday. The United States Supreme Court, after indicating it might be interested in hearing a challenge to the regulations, decided to let them stand.

As is customary when the court declines to hear a case, the justices gave no reasons. There were no published dissents. Perhaps one in a hundred petitions seeking review by the court is granted, meaning that the decision not to hear the case sent no larger message.

The challenge to the rent law was brought by James D. Harmon Jr. and Jeanne Harmon, the owners of a five-story brownstone on West 76th Street near Central Park. They live on the lower floors and rent out the six apartments above them.

Three of those apartments are subject to New York’s rent-stabilization regulations, under which the government sets maximum permissible rent increases and generally allows tenants to renew their leases indefinitely.