PORTLAND, Maine (AP) — Republican U.S. Rep. Bruce Poliquin and three voters sued Tuesday over Maine’s new voting system, used for the first time in U.S. House and Senate elections.

A lawyer for Poliquin’s campaign asked the secretary of state to stop the tabulations to allow a judge to rule, but the secretary declined to stop the process.

Poliquin received the most first-place votes on Election Day and believes he should be declared the winner. But the ranked-choice system requires additional voting rounds because neither he nor Democrat Jared Golden won an outright majority.

The lawsuit, filed Tuesday in federal court, seeks a preliminary injunction. A separate letter was sent to the secretary of state seeking a suspension of tabulations.

“We are continuing to process ballots to complete the tabulation of votes and will continue to do so,” said Kristen Schulze Muszynski, spokeswoman for Secretary of State Matthew Dunlap. “If we receive a court order to halt the process we will review it with our legal advisers.”

The ranked-choice voting system approved by referendum in 2016 lets voters rank candidates from first to last on the ballot. It provides for eliminations of last-place candidates and reallocations of votes to ensure that the winner gets a 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.”

Supporters say the system already has cleared legal challenges.

Several courts, including the 9th U.S. Circuit Court of Appeals in San Francisco, have upheld the constitutionality of ranked-choice voting, supporters said.

The first round of voting on Election Day ended with Poliquin and Golden both collecting 46 percent of the vote, with Poliquin maintaining a slim edge of about 2,000 votes.

Under the system, two independents in the four-way race who together collected about 8 percent of the vote will be eliminated, and their supporters’ second-choice votes will be reallocated.

For now, the voting system is used only in federal races and in statewide primary elections in Maine. It cannot be used in the governor’s race or legislative races because of concerns it runs afoul of the Maine Constitution.

Democratic Gov.-elect Janet Mills has vowed to seek to amend the constitution so the system can be used in all elections.