NEW YORK — Rupert Murdoch’s News Corp. has pulled back on one of the charges in its lawsuit against Time Warner seeking to get the Fox News Channel cleared on TW’s giant cable system in New York City.In a sentence buried in its just-issued 10-K filing, TW revealed publicly for the first time that on March 14 the Fox News Channel “conceded its inability to sustain its breach-of-contract claim and withdrew it.” Sources say News Corp.’s lawyers, after weeks of discovery, had to back off this charge because they couldn’t find a signed contract authorizing carriage of Fox News on TW’s New York system. But a TW spokesman downplayed the importance of the withdrawal because the lawsuit still is on the federal court’s fall docket, with discovery about to begin on Fox’s antitrust claim. The crux of the legal action is the allegation that by keeping Fox News off its Gotham cable system — the largest in the country, reaching 1.1 million subscribers — TW is using monopoly power to protect its three wholly owned news networks: CNN, CNN Headline News and New York 1. The suit also alleges fraud, claiming that by agreeing verbally to take Fox News on many of its cable systems, TW caused News Corp. to spend millions of dollars building a facility in New York on what turned out to be a false pretext. TW’s counterclaim is that it declined to take Fox News, even though the network was offering the unusually gener-ous sum of $10 for each TW subscriber, because the company’s cable system doesn’t currently have the channel ca-pacity to accommodate the 24-hour news channel. However, TW is adding 12 channels to its N.Y. system next fall, so the parties could start new talks about the adding of Fox News in exchange for News Corp.’s dropping the lawsuit. But for now both sides say the hostility is too acute for either of them to be willing to initiate such talks.