The lawsuit asks a federal judge to stop the vote tabulations and to declare ranked-choice voting to be unconstitutional, clearing the way for Poliquin to be declared the victor. The secretary of state declined a separate request to stop the election process without a court order.

The first round of voting on Election Day ended with Poliquin and Democrat Jared Golden both collecting 46 percent of the vote in Maine's huge, largely rural 2nd Congressional District, with Poliquin maintaining a slim edge of about 2,000 votes in unofficial returns.

"I won the election fair and square," Poliquin said Tuesday, declaring the lawsuit is necessary to test the constitutionality of the voting system.

In the lawsuit, Poliquin, who is seeking a third term, and three Republican activists contend he should be declared the winner because he has the most first-place votes. But the ranked-choice system requires additional voting rounds because neither he nor Golden won an outright majority.

The lawsuit says the "foundation of our 'democratic process' is the right of all qualified voters to cast their votes effectively." It suggests that the ranked voting system "denies Plaintiffs the opportunity to cast their votes effectively."