AUGUSTA — At least $2 million has been spent on negative attacks in Maine’s gubernatorial race, the campaigns said Tuesday, and the figure will likely grow in the days left before the election even as voters and candidates themselves decry the mudslinging.

Rival gubernatorial candidates are complaining about negative advertisements, and many voters are expressing disgust over dirty politics. But a political scientist says negative political ads are as old as the Declaration of Independence — and can actually be useful to voters.

Republican Paul LePage’s campaign says more than $1 million has been spent by groups opposing him on mailings or TV ads attacking him, and the total could double by the time voters go to the polls next Tuesday.

Independent Eliot Cutler has accused the Republican and Democratic parties and their supporters of smearing him to the tune of $500,000. Democrat Libby Mitchell’s campaign also says at least $500,000 has been spent on negative and attack ads targeting her — one of which shows mud being splattered on the TV screen.

During a debate last week, independent candidate Shawn Moody challenged his rivals to knock it off, saying voters are “disgusted” by the tone of the campaign.

Fay Sholz, an 80-year-old voter from Hallowell, agrees.

“It’s dirty politics,” Scholz said Tuesday as she waited for a bus in Augusta. “I think it turns people off. They’re like a bunch of gossipy women.”

The meanest, nastiest ads targeting candidates are often aired by the political parties and other organizations with an interest in the outcome of the race.

And they’re not limited to the governor’s race. Television ads and mailers that have been turning up lately sharply criticize — some would say attack — candidates for Congress and the state Legislature.

But negative ads are nothing new and have been a part of American politics since colonial days, said Michael Franz, professor of government at Bowdoin College. And unlike Sholz and other voters, Franz doesn’t think they’ve gotten out of hand. There is just more advertising in general, he said.

The level of general political advertising in America and Maine is growing, “but the proportion that tend to be negative is not all that different year to year,” Franz said.

“It does seem like there are more negative ads because there are, but there are more positive ads too,” he added.

And it’s not all bad. Such negative ads can cause voters to become engaged in the process by looking past the rhetoric and taking a closer look at the issues being raised in the ads, he said.

The son of the late Edmund S. Muskie, a prominent Democratic who served as governor, senator and secretary of state, said his father would not approve of the negativity, including tactics employed by his own party.

“My father would be outraged — and few people could be outraged as forcefully as Ed Muskie — at the kind of campaign that’s being waged in Maine this year by both parties,” said Edmund S. Muskie Jr.