As some officials in New Jersey are pushing to legalize the recreational use of marijuana, the state’s attorney general directed prosecutors on Tuesday to seek to pause any cases stemming from marijuana-related offenses for at least a month, in a move regarded as a possible step toward decriminalizing such offenses.

The attorney general’s announcement comes after Gov. Philip D. Murphy, a Democrat who was elected last year, campaigned heavily on legalizing marijuana and follows an effort by officials in Jersey City to pre-empt state leaders by declaring that municipal prosecutors would use their “broad discretionary powers” to no longer pursue marijuana possession cases as criminal offenses.

In a memo issued on Tuesday, the attorney general, Gurbir. S. Grewal, asked prosecutors in New Jersey to seek adjournments until September in “any matter involving a marijuana-related offense pending in municipal court.” Mr. Grewal had challenged the argument officials raised in Jersey City, but in a statement on Tuesday, his office said he sought the delay while working to “clarify the scope and appropriate use of prosecutorial discretion in marijuana-related offenses in municipal court.”

The attorney general’s move has been welcomed by proponents for changing marijuana laws, including the American Civil Liberties Union of New Jersey, which called it “a step forward.” Even some opponents of legalization praised the decision as a sensible one.