TOKYO (Reuters) - Support for Japanese Prime Minister Shinzo Abe, plagued by accusations of cronyism and cover-ups, fell to 26.7 percent in a survey by private broadcaster Nippon TV released on Sunday, the lowest since he took office in December 2012.

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Abe’s sliding ratings are raising doubts over whether he can win a third three-year term as ruling Liberal Democratic Party (LDP) leader in a September vote he needs to win to stay in office or whether he might even resign before the party election.

The Prime Minister last week denied again that he had intervened to ensure preferential treatment for educational institution Kake Gakuen, run by his friend Kotaro Kake, to set up a veterinary school.

He has also repeatedly denied that he or his wife intervened in a heavily discounted sale of state-owned land to another school operator, Moritomo Gakuen, with ties to his wife.

Another survey released on Sunday by Kyodo news agency put Abe’s support at 37 percent, down 5.4 points.

The polls come ahead of Abe’s summit this week with U.S. President Trump, where he faces a tough agenda including North Korea’s nuclear and missile threat and sticky trade issues.

Former cabinet minister Shigeru Ishiba, who has made clear he wants to challenge Abe for the top post, topped the list of politicians that respondents to the Kyodo survey saw as best suited to become the next premier, with 26.6 percent.

Popular young LDP lawmaker Shinjiro Koizumi, son of ex-prime minister Junichiro Koizumi, ranked second with 25.2 percent, followed by Abe in third place with 18.3 percent.

Former premier Koizumi told reporters on Saturday he thought it would be difficult for Abe to win a third term as LDP leader.

“He has lost trust and whatever he says sounds like an excuse,” he told reporters.