NEW YORK — A federal judge on Monday rejected demands to eliminate toll increases imposed last summer at bridge and tunnel crossings in New York and New Jersey, saying lawyers had failed to back up claims that a bistate agency that raised them was using increased revenues for other projects including the new World Trade Center.

Judge Richard Holwell said in a written ruling that it seemed unlikely that the lawsuit challenging the increases imposed in September will succeed. Still, he allowed the lawsuit to proceed, saying additional evidence can be gathered before he makes a final ruling.

AAA of New York and New Jersey brought the lawsuit against the Port Authority of New York and New Jersey, saying the Port Authority is spending toll revenue on the rebuilding of the World Trade Center. It cited a ruling in another case in which a court found that it was unconstitutional that a fee imposed on ferry passengers between Bridgeport, Conn., and Port Jefferson, N.Y., subsidized services with no actual or potential benefit to ferry passengers.

The judge, though, said the Port Authority has provided financial analyses "strongly suggesting that no toll increases are, or will be, used for the World Trade Center."

Holwell said AAA lawyers had "offered insufficient evidence to counter the Port Authority's financial analyses."

The judge said it would be an "extraordinary and drastic remedy" to roll back the toll increases before both sides can study additional evidence.

Marta Genovese, a spokeswoman for AAA New York, said: "We are pleased that the Court recognized that the financial information submitted by the Port Authority had never been previously disclosed to the public and are looking forward to the opportunity to support our claims with more than just the documents available on the Authority's website."

In a statement, the Port Authority said it was pleased with the ruling.

"The Port Authority has stated all along that the AAA's lawsuit is without merit," it said.