The country's second- and third-largest pay television networks yesterday won Justice Department approval to merge after they agreed to cut out two of the three motion picture distributors who were part of an original merger plan.

The third version of the proposed merger of Showtime and The Movie Channel that has been submitted for Justice Department approval leaves Warner Bros. as part of the deal. But two other motion picture distributors, Paramount Pictures Corp. and Universal City Studios Inc., were forced by antitrust considerations to pull out of the joint venture.

The deal was designed to challenge the pay TV dominance of Home Box Office, owned by Time Inc., which is far and away the industry leader with 12 million subscribers. Showtime, the number two pay TV service, has about 4 million subscribers, while The Movie Channel, number three, has about 2.5 million subscribers. Together, their subscribers amount to about half of HBO's users.

William F. Baxter, assistant attorney general in charge of the Antitrust Division, said the Justice Department rejected the earlier proposals out of concern that a pay TV partnership including three motion picture distributors would have enough market power to push up fees for movies on pay TV. Although that could drive competing pay TV firms out of business, it would not hurt the new venture because it in effect would be paying the uncompetitively high price to another part of the same corporate entity.

That problem would not be present with only one film distributer in the deal, Baxter continued.

Showtime is owned by Viacom International Inc., a cable and programing firm, while The Movie Channel is owned by Warner Amex, a joint venture of American Express and Warner Communications. Warner Bros. is a subsidiary of Warner Communications. Under the proposal, Warner Amex and Viacom each would own 50 percent of the Showtime-The Movie Channel combination, which is likely to run under one management while retaining separate 24-hour-a-day services.