"We offered to pay reasonable increases, but CBS's demands are out of line and unfair and they want Time Warner Cable to pay more than others pay for the same programming," Time Warner Cable said in a statement.
CBS countered, saying that it remained firm in getting fair compensation for its programming. It accused Time Warner Cable of having a "short-sighted, anti-consumer strategy."
Not long after the two sides traded barbs, Time Warner Cable said it halted its plans to drop CBS at the broadcaster's request.
CBS said both sides have agreed to continue negotiations.
Time Warner Cable spokeswoman Maureen Huff said some areas didn't experience a CBS "blackout" and those who did it was "a matter of minutes."
The disagreement centers mainly on how much Time Warner Cable pays for the right to retransmit signals from the CBS-owned stations.
"As we've said, we feel like we should be paid for our programming," CBS chief executive Les Moonves told the Television Critics Association earlier Monday.
Dozens of blackouts have occurred nationwide in fee fights over the years, but many get resolved at the last minute.
Selling retransmission rights has become a big business for broadcasters such as CBS. Research firm SNL Kagan estimates retransmission fees will reach $3 billion industrywide this year and double to $6 billion by 2018.
Time Warner Cable has said it's resisting a fee hike demand by CBS so prices don't go up for customers. CBS said Time Warner Cable isn't agreeing to terms that its competitors have accepted.