OR YEHUDA, Israel — With Prime Minister Benjamin Netanyahu of Israel politically weakened and steeped in legal troubles, a rival from within his conservative Likud party has emerged to challenge his grip on the party leadership.

After two inconclusive elections ended with Mr. Netanyahu unable to form a government, Gideon Saar, a seasoned if staid party veteran, is running against him in a primary leadership contest on Thursday.

Mr. Saar argues that only a leadership change can save the party, and the country, from doom in the unprecedented third election set for March.

“We see that we are going down in poll after poll,” Mr. Saar told supporters at his primary campaign launch last week in a wedding hall in Or Yehuda, a Tel Aviv suburb and Likud stronghold. “If we do not bring about a change, we are very close to getting a left-wing government, a government that will endanger everything we hold dear.”