By Jonathan Stempel

NEW YORK (Reuters) - A federal judge on Thursday approved settlements for 78 cleanup workers who claimed to have suffered respiratory and gastrointestinal illnesses while working in buildings near the World Trade Center site after the Sept. 11, 2011 attacks.

The workers, whose settlement terms were not made public, are among roughly 1,000 to pursue damages claims in Manhattan federal court for having cleaned more than 100 privately-owned buildings in downtown Manhattan.

These 1,000 workers brought claims against approximately 345 building owners, managing agents, tenants, environmental consultants and contractors.

About one-third of the workers have settled, and another 400 to 500 could follow within a month, according to Paul Napoli, a lawyer for the 78 settling workers.

U.S. District Judge Alvin Hellerstein in Manhattan, who oversees much of the Sept. 11 litigation, approved the latest settlements.

He said they compared "favorably," both individually and as a whole, with a $716 million accord he approved in 2010, which covered more than 10,000 people who worked at the World Trade Center site and brought claims against the city and contractors.

In a phone interview, Napoli said the 78 workers claimed to have developed symptoms such as asthma, breathing difficulty, excessive coughing, dizziness and fatigue.

The 78 workers settled claims against 134 defendants. Twenty-six workers resolved all claims, and 52 resolved many claims.

"These settlements with these defendants have been hard fought, and it is finally bringing closure in one of the last vestiges of this litigation," Napoli said.

The case is In re: World Trade Center Lower Manhattan Disaster Site Litigation, U.S. District Court, Southern District of New York, No. 21-mc-00102.

(Reporting by Jonathan Stempel in New York; Editing by Tom Brown)