TOKYO — Most Japanese think Prime Minister Shinzo Abe bears some responsibility for altered documents at the center of suspicions of a cover-up linked to cronyism, according to opinion polls on Sunday, with one showing his support falling to the lowest of his tenure.

In his worst crisis since taking office in 2012, Mr. Abe and Finance Minister Taro Aso have been under fire since the finance ministry said on March 12 it had altered records relating to a discounted sale of state-owned land to school operator Moritomo Gakuen, which had ties to Mr. Abe’s wife, Akie. References to Mr. Abe, his wife, and Mr. Aso were removed from the Finance ministry’s records of the sale, copies of documents released by the ministry showed. Both men have denied any wrongdoing in the affair.

But 66.1% of respondents to a poll conducted by Kyodo news agency on Saturday and Sunday said they felt the premier had some responsibility for the altered documents.

Only 25.8% said they thought he didn’t.

A Mainichi Shimbun poll similarly found 68% believe Mr. Abe bears responsibility.

Protesters have flocked to the streets by the prime minister’s office every night since the ministry admitted altering the documents, with some 2,000 on Friday calling for Messrs. Mr. Abe and Mr. Aso to resign.

A Nippon TV poll found Mr. Abe’s support crumbling some 14 points from last month to 30%, the lowest for that poll in Mr. Abe’s more than five years in office and less than half the peak of 66% in April 2013, when his easy-money “Mr. Abenomics” policies were dramatically starting to lift Japan out of decades of deflation.

Respondents not supporting Mr. Abe jumped 16 points to 53% in the survey conducted over the weekend, also a record for the Nippon TV poll.

In the Mainichi poll, Mr. Abe’s support fell 12 points to 33%, while those not supporting him climbed 15 points to 47%. The Kyodo poll showed Mr. Abe’s support slipping by 9.4% to 38.7% in the past two weeks, while 48.2% said they did not support him.

Opposition parties are calling for Mr. Aso to resign, while the affair could dash Mr. Abe’s hopes of winning a third three-year term as head of his Liberal Democratic Party in a September party leadership election. Mr. Abe took office in December 2012.

The Nippon TV poll found 61% believe Mr. Aso should resign, about double the 29% who don’t think he should. In the Mainichi poll, 54% favored resignation versus 32% who did not think he should step down.

Mr. Aso has repeatedly refused to resign and has said that the responsibility for the land sale lay with Nobuhisa Sagawa, who stepped down as tax chief 10 days ago. Mr. Sagawa headed the division that submitted the documents before he became tax agency chief in July.

Almost two-thirds in the Nippon TV poll think Finance ministry officials doctored the documents either because of political pressure or to anticipate what the Mr. Abe administration wanted.

Just 14% of those polled accepted the official explanation that the alterations were meant to match the parliamentary testimony of a senior ministry official on the matter.

Mr. Aso is skipping a meeting of G20 finance leaders this week. A ruling party source told Reuters this was so he can address parliament on Monday about the scandal. — Reuters