Lifetime said in a statement Friday that the matter involves federal copyright law.
A New York state judge has issued an injunction preventing the show's producers, the Weinstein Co., from moving forward on an agreement to bring the series to Lifetime. The show's first five seasons have been on NBC Universal's Bravo, and NBCU is seeking to keep it on one of its networks.
Separate from the injunction, NBCU was moving forward with a breach of contract case in New York State Supreme Court against Weinstein, charging that it had the right to match the offer Weinstein received from Lifetime for "Runway." When issuing the injunction, the judge indicated that NBCU was likely to prevail and be able to keep "Runway."
"We continue to believe that Lifetime has rights superior to NBCU's claimed right of first refusal on future cycles of 'Project Runway,'" Lifetime said.
NBCU issued a statement saying that Lifetime is engaged in a delay tactic, and that it "will vigorously fight this eleventh-hour move" and try to have the case returned to state court.
A call to the Weinstein Co. was not immediately returned.