At first, voters seemed not to be much bothered by the financial scandal because much of the money came from Mr. Hatoyama or his mother, a wealthy heiress. But now, analysts say, it is precisely that explanation that is starting to cool public opinion of the prime minister. By highlighting the considerable wealth of his family, the scandal is starting to raise doubts about how in touch he is with the worsening economic plight of average Japanese.

According to reports in Japanese newspapers, Mr. Hatoyama will soon deliver a written statement to Tokyo prosecutors in which he will deny knowledge of some $4 million in donations that prosecutors say were improperly reported, sometimes in the names of dead people. The reports say he will also tell prosecutors that he did not know of millions of dollars more that his group received from his mother. Mr. Hatoyama’s office said it had no knowledge of the statement.

The reports said that prosecutors were considering whether to charge one of Mr. Hatoyama’s former political secretaries for misreporting the funds, but that they would not charge the prime minister with a crime.

Still, just the fact that Mr. Hatoyama could get mired in such a campaign finance scandal has already hurt his credibility as a reformer, analysts say.

Polls show that Mr. Hatoyama’s approval ratings are slipping from their highs of more than 70 percent after he took office in September. A poll released Monday by Japan’s national public broadcasting corporation, NHK, found that 56 percent of 1,111 voters questioned by telephone from Dec. 11 to 13 said they approved of him, with 34 percent saying they did not approve. The poll gave no margin of error, as is customary here.