NEW YORK — The summer box office continued to lack mojo, as the R-rated “Sex Tape” failed to turn on moviegoers on a weekend where “Dawn of the Planet of the Apes” maintained its rule.

20th Century Fox’s science fiction sequel outmuscled a trio of new films to top the North American box office for the second-straight week with $36 million, according to studio estimates Sunday. The acclaimed sequel to 2011’s reboot of the chimp franchise has now made $139 million domestically in two weeks.

Additional Images

Andy Serkis plays Caesar in a scene from “Dawn of the Planet of the Apes,” from Twentieth Century Fox. The Associated Press

A scene from “The Purge: Anarchy.” The Associated Press

Its closest completion over the weekend was the home-invasion horror thriller “The Purge: Anarchy,” written and directed by James DeMoncaco. Universal’s low-budget sequel to last year’s surprise hit, “The Purge,” opened with $28.4 million, down from the $34.1 million the original scared up on opening weekend.

Nikki Rocco, head of distribution for Universal, though, noted the stronger competition this time around and the overall “depressed” business at movie theaters. Weekend revenue was down 24 percent from the same weekend last year, continuing a cold summer for Hollywood that’s more than 20 percent off the pace of summer of 2013.

But “Anarchy,” which imagines an America where all crime is legal for 12 hours every year, was made for only $9 million, making it immediately profitable for Universal. Such success is the envy of most movies, particularly Sony’s “Sex Tape,” a starrier, more expensive release that opened with $15 million.

The Jason Segel, Cameron Diaz R-rated comedy failed to turn on moviegoers or critics. “Sex Tape,” in which a married couple makes a pornographic home video to stoke the flames of their lagging sex life, came in fourth place behind Disney’s “Planes: Fire & Rescue.” The animated sequel to 2013’s “Cars”-offshoot, “Planes,” opened with $18 million.

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