JUNEAU, Alaska (AP) — A federal judge on Sunday dismissed a Justice Department lawsuit seeking to block certification of Alaska’s U.S. Senate race if Republican incumbent Dan Sullivan loses.

Sullivan, an ally of President Donald Trump, faces Democratic former U.S. Rep. Mary Peltola in one of the country’s most closely watched races, with Senate control at stake. Tuesday’s ranked-choice election also includes two candidates who have done little campaigning, one of whom shares the incumbent’s name. It was that candidate's presence on the ballot that prompted Trump to push for the lawsuit out of fear he would siphon votes from the incumbent.

The lawsuit, filed less than two weeks before the election and as early voting was underway, called for an investigation into whether votes for retired teacher Dan J. Sullivan were intended for the senator. The state said the case lacked merit and argued there would be no way to determine that without violating voter privacy.

U.S. District Court Judge Sharon Gleason wrote in the order that the relief the United States seeks is “infeasible” because many voters have already cast their ballots.

“More fundamentally, the United States provides no workable plan as to how it proposes to segregate ballots cast for Daniel J. Sullivan on Election Day and then conduct a court-ordered unspecified 'investigation' of those ballots in a manner that would preserve voter secrecy,” she wrote.

The Department of Justice, attorneys for the state and Peltola’s campaign did not immediately return messages seeking comment.

Senator says he expects ‘to lose a lot of votes’ to the other Dan Sullivan

Peltola's campaign and the Democratic Senatorial Campaign Committee argued that the case lacked any legal basis and amounted to interference. The senator and his allies, including Trump, for months have portrayed Dan J. Sullivan as a sham candidate intent on confusing voters and helping Peltola.

Earlier Sunday, Sen. Sullivan told CNN that he thought the presence of the second Sullivan on the ballot would affect the election.

“I’m sure I’m going to lose a lot of votes to that trickery,” he said.

He also said he doubted claims by Peltola that she had no idea her top political aides were involved in recruiting Dan J. Sullivan to run as a way to confuse voters.

“There is no way this went on for a year that they weren’t informing her,” Sullivan told CNN’s “State of the Union.” “She got caught lying, and she’s still lying to the Alaskan people, the media, to all of us.”

The senator's campaign did not immediately respond to a request for comment on the Sunday court ruling.

In the week before Election Day, The New York Times reported that Peltola’s campaign was involved in efforts to recruit the second Sullivan. Dan J. Sullivan in June, shortly after entering the race, said he’d had no contact with the campaign about running. He has not responded to multiple messages over the past few days.

Peltola’s campaign responded to the Times story by saying it had no involvement in the campaigns for either Sullivan: "I am not interested in tricking voters,” Peltola said during a recent campaign event.

Multiple investigations look into whether Dan J. Sullivan was recruited as a decoy candidate

State courts, including the Alaska Supreme Court, rejected Republican-backed efforts to block the retired teacher from the August open primary ballot on which he appeared as Daniel J. Sullivan Jr., with no party affiliation. The senator was listed as Dan S. Sullivan, Republican and incumbent.

Both Sullivans appear the same way on the general election ballot. Peltola placed first in the primary, followed by the senator. Dan J. Sullivan received about 2.5% of the primary vote, but that was enough to finish within the top four and qualify for the Nov. 3 ranked-choice election.

Attorneys for the Alaska Department of Law represented state elections officials in the case and asked Gleason, who was appointed by former Democratic President Barack Obama, to toss the lawsuit. They filed a scathing response to the federal government’s complaint, calling it “meritless.”

Alaska also said the state had taken “significant steps” to distinguish the two Sullivans on the ballot. Voters who still might be confused could ask for help or look up candidate biographies and other information in state-distributed election pamphlets.

Republicans, including ones working with Trump, also have a long history of backing decoy candidates in elections. The governor, a Republican, has ordered an investigation and suggested he may not certify a possible Peltola victory.

In her ruling, Gleason wrote that the Trump administration’s attempt to block certification ran counter to the Constitution, which gives states the authority to run elections. She also cited the Supreme Court’s Purcell principle, which holds that federal courts should generally not change election rules too close to an election.

On Thursday, the Justice Department escalated a criminal investigation over the presence of Dan J. Sullivan on the Alaska ballot, issuing a raft of new grand jury subpoenas, a person familiar with the matter told The Associated Press. The FBI also has begun contacting people who donated to him, some of whom told the AP that the agents were asking if they had been misled about which candidate they were supporting.

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Associated Press photographer Lindsey Wasson in Anchorage, Alaska, and AP writer Ali Swenson in Washington contributed to this report. Riccardi reported from Washington.