Past inquiries stretching over Mr. Netanyahu’s more than two decades in public life have examined his family trips and home expenses without resulting in charges. But allies and enemies alike were already saying on Tuesday that this case could be different.
The three-hour police interrogation at his official residence on Monday night came at a high-profile moment for Mr. Netanyahu on the international stage.
After years of grinding battle, he has engaged in a guns-blazing war with President Obama during the president’s final weeks in office. At the same time, Mr. Netanyahu has been warmly embraced by President-elect Donald J. Trump, presenting a closer alignment than any other president-prime minister pairing in modern times.
A conservative with a stable governing coalition, Mr. Netanyahu emerged from the police interrogation on Monday with a defiant blast at left-wing elites and the news media for prematurely counting him out. Appealing to supporters on the right, he dismissed the allegations against him, insisting they will all “come to nothing because there is nothing.”
But the attorney general, Avichai Mandelblit, who was Mr. Netanyahu’s choice for the post after a tour as his cabinet secretary, has been a paragon of caution, taking months to turn a preliminary inquiry into a criminal investigation, something that Israeli legal and political commentators said added weight to the suspicions.
“Mandelblit tried doing everything he could so as not to reach the point of having Netanyahu questioned as a suspect,” Amir Oren, a columnist, wrote in the Haaretz newspaper on Tuesday. “If, after all his contortions and twists, the A.G. was forced into ordering an investigation that he was hoping to shelve, the default option from here on is an indictment.”
After the police investigators left Mr. Netanyahu’s home late Monday, Mr. Mandelblit issued a statement close to midnight, vaguely outlining the contours of the case. It said Mr. Netanyahu was suspected of receiving gifts and benefits.
By early Tuesday, Israelis were debating how all this might affect Mr. Netanyahu, whether sitting prime ministers should even be investigated, and if so, at what point they should resign.
The months of multiple inquiries have centered on issues involving “moral integrity” — a term that legal experts said could include suspicions of breach of trust, conflict of interest and bribery.
Much of Mr. Mandelblit’s statement was devoted to prior cases that were closed because of lack of evidence of crimes, including a travel expense scandal known as Bibi Tours, using Mr. Netanyahu’s nickname, and one about campaign funding in 2009.
Mr. Netanyahu, who is serving his third consecutive term since that election, and his fourth over all, denounced those inquiries in a Facebook post.
“Bibi Tours — nothing! Claim of forbidden election funding — nothing!” he wrote, describing reports in the Israeli news media over the years as “daily persecution of me and my family” and “complete gibberish.”
Israeli law requires a prime minister to resign if convicted of serious crimes. But in a precedential ruling in 1993, the Israeli Supreme Court determined that a cabinet minister, Aryeh Deri, had to resign immediately after the attorney general submitted an indictment against him for corruption.
“If everyone who faces an investigation would have to resign, this could turn into a tool used to politically destroy others,” Ayelet Shaked, the justice minister, told Israel Radio. “This is why the idea that resigning should only be after an indictment is a correct one,” she added.
Monday was not the first time Mr. Netanyahu had been questioned as a criminal suspect while in office. During his first term, in the late 1990s, he was queried in a case that involved the appointment of an attorney general as part of what the police said was a political deal involving Mr. Deri. Mr. Netanyahu was never charged in that case, nor in several others for which he was investigated while out of office.
Other Israeli prime ministers, too, have been the subject of police investigations into allegations of campaign irregularities and corruption. Ehud Barak and Ariel Sharon were both questioned. Mr. Netanyahu’s predecessor, Ehud Olmert, was forced from office in 2008, even before any charges were filed against him, and became the first former Israeli prime minister to enter prison. He is serving a 19-month term for bribery and obstruction of justice.
Moshe Katsav, a former president, was recently released from prison after serving five years of a seven-year term for rape.
Some of Mr. Olmert’s supporters felt he was the victim of an overzealous state prosecutor, though many Israelis take pride in the fact that nobody is immune from the law.
But with Netanyahu loyalists asserting that he is the victim of a political witch hunt, some right-wing legislators are now trying to advance a bill that would ban criminal investigations of incumbent prime ministers. (Any such legislation would likely come too late to spare Mr. Netanyahu.)
Critics of the bill argue that such a ban would be problematic in a small country like Israel, and with a political system that has no term limit for prime ministers.
“If prime ministers knew there would be an investigation only after their term was over, they would turn the prime minister’s office into a safe haven and use the powers and resources of the state to extend their stay in office and avoid prosecution,” said Yohanan Plesner, the president of the Israel Democracy Institute, a nonpartisan research center in Jerusalem.
Mr. Plesner, a former Parliament member, added that suspicions would still surface in the news media and if they were not formally investigated, public trust in political institutions could erode.
When Mr. Olmert was under investigation, it was Mr. Barak, then his defense minister — though from a different political party — who pushed him to leave office. Israel’s coalition governments have an inherent weakness, in that parties participating in the coalition are often also political rivals competing for votes in the next election.
So far Mr. Netanyahu’s party and coalition partners appear to be backing him, either voicing support or remaining silent.
But the investigation could last for months, if not more, and that could create political strain.
For now, Mr. Plesner said, “whoever is critical of Mr. Netanyahu will use this to continue to be critical, and his supporters will find their ways to interpret it.”