In televised remarks on Monday afternoon, Mr. Netanyahu told legislators from his conservative Likud Party in Parliament, “We hear the celebratory spirit and winds blowing through the television studios and in the corridors of the opposition.”

“Hold off the celebrations; don’t rush,” he added. “I’ve told you before and will tell you again — this will come to nothing, because there is nothing.”

Mr. Netanyahu is serving his third consecutive term in office, and his fourth over all. He has exuded confidence lately, lashing out at journalists who have been critical of him, talking up Israel’s diplomatic and economic achievements, and calling in the United States ambassador to Israel, Daniel B. Shapiro, for a dressing down late last month after the Obama administration decided not to use its veto to shield Israel from a United Nations Security Council resolution that condemned Israeli settlement construction in the occupied West Bank and East Jerusalem.

Mr. Netanyahu, generally a popular prime minister, has developed a combative relationship with the local mainstream news media. After years of tension with the Obama administration, he also appears buoyed by the prospect of a partnership with President-elect Donald J. Trump, who seems more sympathetic to Israeli government policies on issues like settlements.

For Mr. Netanyahu’s opponents, the prospect of a possible indictment has provided a glimmer of hope, even though elections are not scheduled until late 2019.

“This creates an unusual dynamic in Israeli politics,” said Nahum Barnea, a political columnist for the newspaper Yedioth Ahronoth and a critic of Mr. Netanyahu. On the one hand, Mr. Barnea said, there were already signs that Netanyahu loyalists would try to promote legislation banning investigations of sitting prime ministers. On the other, he said, the question of who might succeed Mr. Netanyahu, who has no natural heir in his party, was bound to be raised.

Opposition leaders were fairly subdued in their initial response. Isaac Herzog, the leader of the Zionist Union and of the opposition in Parliament, said it was “a tough day for Israel when a prime minister is under investigation.”