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.

The lawsuit, filed less than two weeks before the election and with early voting 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. She said the cast ballots been commingled to the point where the identity of the person who cast each ballot can’t be determined.

“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.

THIS IS A BREAKING NEWS UPDATE. Check back for updates. AP’s earlier story follows below.

Republican Sen. Dan Sullivan said Sunday that he doubted claims by his Democratic opponent that she had no idea her top political aides were involved in recruiting a retired schoolteacher also named Dan Sullivan onto the ballot to confuse voters in a race that could determine which party controls the Senate.

Republicans have long suspected that Mary Peltola, a former congresswoman, and her campaign were behind the presence of the second Sullivan on the ballot. They say their suspicions were confirmed by a New York Times report last week that was based on interviews with Peltola's ex-campaign manager, text messages and campaign finance documents showing that an operative trying to recruit decoy candidates was paid by a group backing Peltola.

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

Peltola has insisted she had nothing to do with recruiting the other Sullivan and has called the attention on it a “distraction” from the main issues facing Alaskans of high prices caused by the war in Iran launched by Republican Donald Trump. Her campaign has also denied involvement, as has the national Democratic operation that focuses on Senate races, the Democratic Senatorial Campaign Committee.

Before a rally Friday, Peltola was asked if it was possible someone on her campaign was involved in recruiting the other candidate: “I have no idea,” she told KTUU. “I honestly have no idea.”

The second Sullivan, who is listed on the ballot as Daniel J. Sullivan Jr. while the senator is listed as Dan S. Sullivan and marked as a Republican incumbent, has long insisted he ran on his own accord.

Trump, who ordered his Department of Justice to file a lawsuit to stop certification of a possible Peltola win, called for the Democratic candidate to be prosecuted after the Times story was published. Federal agents descended on Alaska and issued subpoenas in the case, even though 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.

South Carolina Sen. Tim Scott, who heads the GOP group that focuses on Senate races, said on NBC's “Meet the Press” that criminal charges might make sense.

"We know that it is criminal for candidates to work in collusion with other parties to confuse voters,” he said.

Rep. Jamie Raskin, D-Md., said candidates with the same name as others on the ballot “happens all over the place,” though he said promoting such a strategy is not something he would do.

“It’s stupid politics,” he told NBC. “Nobody would do that, and Mary Peltola has said she had nothing to do with it.”

Sen. Bernie Sanders agreed. “What the Democrats did in Alaska seems to me to be pretty dumb," the Vermont independent said on CBS' “Face the Nation.” "It’s not illegal. It’s what happens in every election.”

Sullivan, a former Alaska attorney general, said he would “let the lawyers” determine whether crimes were committed. He did say he thought the presence of the second Sullivan would affect the election.

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

Sullivan also demurred when asked if he would urge the state not to certify a Peltola win, before saying, "I'm going to accept the results of the election.”

Both candidates have spent the final days campaigning through Alaska's vast landscape.

On Saturday night, Sullivan handed out candy at a “trunk-or-treat” event at a recreation center north of Anchorage, where he quipped his costume was “the real Dan Sullivan.”

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Associated Press photographer Lindsey Wasson in Anchorage, Alaska, contributed to this report.