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CBS’s Showtime is pulling popular shows such as “Californication” and “Dexter” from Netflix, just days after the streaming video service kicked off a rivalry with pay-TV networks by cutting a deal to produce original programming.

Showtime confirmed yesterday it will hold back some current shows from Netflix but make them available to subscribers who pay for Showtime’s own streaming service.

“Current and past seasons of our original series will be available to our authenticated subscribers via our TV Everywhere service Showtime Anytime,” a Showtime spokeswoman told The Post.

The move is an about-face for Showtime, which premiered “United States of Tara” and “The L-Word” on Netflix to much fanfare in 2009.

Gone from Netflix are two seasons of “Californication” and one season of “Dexter,” but it gets to keep “The Tudors” and adds a new series, “Sleeper Cell.”

While the change appears relatively minor, it highlights the increasing pressure on content players to keep their cable and satellite distribution partners happy.

Time Warner’s HBO, for instance, won’t do business with Netflix, even though rivals Showtime and Liberty Media’s Starz have both done deals with the service.

With 20 million subscribers and a soaring stock, Netflix is seen as a growing threat to Hollywood execs who are responding by limiting its access to newer shows.

Last week, Netflix cut a deal to obtain “House of Cards,” a new series from director David Fincher. The estimated $100 million deal was a departure for Netflix, which has heretofore relied on licensing content from others.

A Netflix spokesman disputed Showtime’s characterization of the situation, saying that negotiations are in flux.

“Netflix may or may not renew with Showtime,” a Netflix spokesman said. “Titles expire and migrate on and off Netflix as part of the ebb and flow of licensing. Nothing from Showtime is being taken down.”

Showtime sources said the streaming part of their deal is concluded, while talks continue for a DVD agreement.

Meanwhile, Netflix suffered an outage on Tuesday night and said it would credit users for the disruption, but even that didn’t hurt the highflying stock, which gained 3.5 percent to $229.06 yesterday. catkinson@nypost.com