A set of city lawsuits against online vendors who sell tax-free cigarettes will move forward after a federal court yesterday reversed earlier decisions by lower courts to dismiss them.

The city filed the four lawsuits in 2003 that argue that the owners of a group of Web sites that sell cigarettes violated the Jenkins Act, which requires that businesses report out-of-state tobacco sales to state tax authorities, by marketing their product as tax-free.

In a 2-1 opinion, the 2nd U.S. Circuit Court of Appeals decided that the city was able to pursue claims under the Racketeer Influenced and Corrupt Organizations Act, better known as RICO, but that separate claims regarding violations of state consumer protection laws would have to be referred back to state courts for guidance.

In a statement, Mayor Bloomberg praised yesterday’s decision.

“We will continue moving forward vigorously against those who break the law and deprive the City of vitally needed tax dollars — especially when such lawbreakers also undercut public health,” Mr. Bloomberg said, “I once again urge Albany to take decisive action to crack down on cigarette bootlegging, beginning with collecting the state sales tax on cigarettes sold on Indian reservations.”