A state appeals court declined on Thursday to stop New York City from forcing chain eateries to post a saltshaker icon next to menu items that exceed the total daily recommended sodium allowance, about a teaspoon.

The court’s one-page order, lifting a different court’s temporary restraining order sought by a restaurant trade group, means that eateries with 15 or more locations nationwide — about 3,000 locations in the city — must begin complying by June 6 or face fines, according to Mayor Bill de Blasio’s office.

The administration had opposed efforts by the National Restaurant Association to block the regulation.

Under the rule, the black-and-white saltshaker warning must appear on food menu items that surpass the recommended daily limit of 2,300 milligrams of sodium. Some eateries have already begun posting the warnings.

A spokeswoman for the restaurant association, Christin Fernandez, said the group is continuing to appeal and expects the case to be heard in the fall.

Fernandez said Thursday’s court ruling “will force the men and women that own New York City’s restaurants to start complying with this unlawful and unprecedented sodium mandate before the court has the chance to rule on the merits of our appeal.”

The courts still must rule on the merits of the case, which seeks to toss the sodium rule.

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De Blasio on Thursday called the city rule “a common sense regulation that will help New Yorkers make better decisions and lead healthier lives.”

He said, “New Yorkers deserve to know a whole day’s worth of sodium could be in one menu item, and too much sodium could lead to detrimental health problems, like high blood pressure, heart disease and stroke.”

The rule will be enforced by city inspectors, who can fine an eatery for three types of violations: failing to post the icon, printing it too small or declining to post an additional warning statement explaining the rule. Each carries a $200 fine. A spokesman for the mayor said enforcement would begin June 6.

Efforts to regulate what people eat and what they know about their food — including rules to ban trans fats and require calorie counts — began in earnest under de Blasio’s predecessor, Michael Bloomberg. Those rules withstood challenges, although Bloomberg’s bid to regulate soda sizes was rejected by the state’s highest court.

The decision was issued by justices Rolando T. Acosta, Dianne T. Renwick, Sallie Manzanet-Daniels, Barbara R. Kapnick and Troy K. Webber of the First Judicial Department’s Appellate division.