The cable company said it had accepted New York Congressman Steve Israel's written request for a cooling-off period in current negotiations with News Corp over fees to broadcast Fox TV programs.
Time Warner urged Fox to do the same.
The two sides are currently facing a midnight deadline to reach a deal. About 13 million Time Warner Cable subscribers will lose Fox programing without an agreement.
News Corp wants Time Warner Cable to pay $1 per subscriber per month for the right to carry Fox Networks' free-to-air broadcast shows such as American Idol, The Simpsons and House, as well as sports programing like college and NFL football games.
But Time Warner Cable has balked at the so-called retransmission fee. Its executives privately point to deals with smaller affiliate TV broadcasters at around 20-25 cents a subscriber.
While $1 per subscriber does not sound like much, Time Warner Cable is wary of setting a precedent. Besides Fox, the other three major U.S. broadcast networks -- CBS Corp's CBS, Walt Disney Co's ABC and General Electric Co's NBC -- will all be pushing to be paid cash per subscriber as their advertising-reliant business suffers.