JERUSALEM — A leading rival to Prime Minister Benjamin Netanyahu from within his own party rebuked the longtime Israeli premier on Saturday for calling his indictment on corruption charges an “attempted coup” and demanded a primary election be held to replace Mr. Netanyahu and “save the country.”

The broadside by Gideon Saar, a popular and ambitious former minister who said he would be a candidate for Mr. Netanyahu’s job, compounded the political crisis confronting the prime minister and signaled what could be a bitter internecine fight for control of Likud, the right-wing party that has led Israel for most of the past four decades.

“That isn’t an attempted coup,” Mr. Saar said of Mr. Netanyahu’s indictment by the Israeli attorney general. “Not only is it wrong to say that, it’s also irresponsible to say that. It’s completely out of touch.”

At the same time, Benny Gantz, the centrist former army chief from the Blue and White party who defeated Mr. Netanyahu in a Sept. 17 election but was unable to form a government, called upon the newly weakened prime minister to go along with an idea he has so far refused to entertain: allowing Mr. Gantz to serve as premier for two years, after which, if Mr. Netanyahu were acquitted, Mr. Gantz would allow him to resume his post.