JERUSALEM — Police investigators arrived at the official residence of Prime Minister Benjamin Netanyahu on Monday evening to question him, indicating that Israel’s attorney general has upgraded a long-running graft inquiry into a criminal investigation.
The Israeli news media has been awash in recent days with reports that a criminal investigation was coming, saying that Mr. Netanyahu is suspected, among other things, of having received illicit gifts and favors. On Monday evening, Channel 2 News showed images of a police car pulling up at the residence.
The Israeli police and the Justice Ministry have refused to confirm or deny the reports, saying only that a formal announcement was forthcoming. Aides to the prime minister also declined to comment.
Mr. Netanyahu, who has been subject to police inquiries in the past that ended without charges, has vehemently denied any impropriety. “This will all come to nothing, because there is nothing,” he has said repeatedly of the latest accusations.
Local news outlets say the investigators are focused on two separate cases, one more serious than the other, but they have offered little detail on the more serious one.
The less weighty one, according to reports in the newspaper Haaretz and other outlets, concerns favors for Mr. Netanyahu, and possibly for members of his family, given by Israeli and foreign businessmen. The Israeli police took testimony from Ronald S. Lauder, a conservative American businessman and philanthropist, and a close friend of Mr. Netanyahu’s, when he came to Israel in late September to attend the funeral of Shimon Peres, the former prime minister and president.
Mr. Netanyahu’s office, suggesting that he is the victim of a witch hunt, issued a statement over the weekend berating the news organizations for what it described as premature and politically motivated reports. “Try to replace the prime minister at the ballot boxes, as is accepted in democracies,” it added.
Mr. Netanyahu, the leader of the conservative Likud Party, is serving his third consecutive term in office, and his fourth overall. 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.
Israeli prime ministers are not obligated to step down while under investigation, unless they are charged with a crime. Nonetheless, the accusations could chip away at Mr. Netanyahu’s standing. His predecessor, Ehud Olmert, was forced from power in 2008 under the weight of police investigations and accusations of corruption, although he remained in office as a caretaker prime minister until early elections could be held in 2009.
In February, Mr. Olmert became the first former Israeli prime minister to enter prison. He is serving a 19-month term for bribery and obstruction of justice.
Since the 1990s, Mr. Netanyahu’s political career has been dogged by inquiries into his conduct, and that of people around him, though no charges have been filed against him. The inquiries have ranged from scandals involving travel expenses and garden furniture — the Netanyahus were suspected of having switched a new set bought for the prime minister’s official residence with an identical, old set in their private home in Caesarea — to a more recent one involving a billion-dollar deal with Germany for the acquisition of submarines.
That agreement came under scrutiny after it became known that Mr. Netanyahu’s personal lawyer also represents the Israeli agent of the German shipyard that builds the submarines, and other naval equipment purchased by Israel, giving rise to suspicion of a conflict of interest.
In that episode, too, Mr. Netanyahu and the lawyer, David Shimron, have denied any wrongdoing.