"We have agreed to an extension with CBS until Friday, Aug. 2 at 5 p.m. ET, while we continue negotiations, Time Warner said in a statement Tuesday.
"There's progress being made and hopefully we don't go dark," CBS CEO Leslie Moonves told reporters in Los Angeles.
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"We still believe our content is worth a lot of money."
Negotiations between CBS and Time Warner Cable continued after midnight in New York, according to a spokeswoman for the cable operator. Time Warner said it had relented "at the request of CBS."
The blackout would have affected an estimated 3.5 million customers in cities such as New York, Los Angeles and Dallas.