American Express Co. said yesterday it had agreed to sell Warner-Amex Cable Communications Inc., one of the nation's largest cable-television companies, to Time Inc. and Tele-Communications Inc. for $1.35 billion.

But the deal is contingent on acceptance of the offer by Amex's partner in the company, Warner Communications Inc. Warner, which has reportedly resisted a sale in the past, yesterday had no comment on the American Express announcement.

Under the proposal, Time and TCI would join forces to pay $850 million for Warner-Amex, and take over its $500 million in debt -- although the total value of the offer could be sweetened with payment of some of the proceeds from the expected sale of Warner-Amex's share of the cable-TV programming services Showtime/The Movie Channel and MTV music television.

Analysts saw the unusual move as an attempt by American Express to force Warner to let Amex out of the Warner-Amex partnership, which has always been a money-loser.

"We know what American Express wants -- they want out," said analyst Mark Riely at F. Eberstadt & Co. "The question is what Warner is up to."

Riely said Warner might make a counteroffer to purchase American Express's half of the 6-year-old partnership, or might seek another bid to top that of Time and TCI. "This is not to say this is going to be the last bid," he said.

One possible offer could come from Viacom International Inc., which reportedly put in a bid of $700 million for Warner-Amex several weeks ago. A Viacom spokesman declined comment on the situation.

The combination of Time, TCI and Warner-Amex would create a cable television powerhouse, serving nearly 20 percent of the nation's cable-TV viewers. Englewood, Colo.-based Tele-Communications is the nation's largest cable-TV company, with 3.6 million subscribers, while Time's American Television and Communications cable division has 2.6 million subscribers and Warner-Amex has 1.2 million.

The merger also has the potential to give Time a dominant position in cable-TV programming. The company already owns Home Box Office Inc., the most popular pay-television service, as well as Cinemax, another movie channel, while Warner-Amex owns 19 percent of Showtime/The Movie Channel, the No. 2 pay cable network, and 75 percent of the extremely popular MTV music-video network.

But Time and TCI said they have no interest in Warner-Amex's programming services, and indicated that they would sell MTV and Showtime/The Movie Channel -- the latter because of possible antitrust problems. The agreement with American Express announced yesterday includes the possibility that Time and TCI would share with Warner and American Express some of the proceeds of the sale of the Warner-Amex programming services. That could increase the overall value of the deal.

Warner-Amex was formed in December 1979 when American Express bought a half-interest in the Warner Cable Co. for $175 million. The companies have continued to pump hundreds of millions of dollars into the venture with little return.

In the past year, under the leadership of former Transportation secretary Drew Lewis, the company has undergone stringent cost-cutting, consolidating operations, reducing corporate overhead and laying off dozens of employes.

Last November, Lewis said in a letter to employes, "Looking at where we are today, I believe that we have made tremendous progress and are well on the road to profitability."

American Express has indicated its desire to drop out of the Warner-Amex partnership for some time. Time and TCI first showed their interest in Warner-Amex two weeks ago with a $750 million offer for the company, and while Warner said at that time it was evaluating the offer, American Express said it was "favorably disposed" toward that offer and proposed working out final details, culminating in yesterday's announcement.