The administration of United States President Donald Trump has stepped up its investigation into a US Senate race in the state of Alaska, where it says the Democratic Party put up a sham candidate to confuse voters so the Republican candidate would lose.

Federal prosecutors sent so-called “target” letters to a number of people on Tuesday, including attorney Marc Elias, who has represented the Democratic Party, warning them that it has gathered enough evidence linking them to a possible crime that it regards them as possible defendants in a future indictment.

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In a statement on Tuesday, Elias said, “No one should be surprised that President Trump’s Department of Justice is targeting me and my law firm on Election Day.”

“We will not be intimidated by a sham investigation,” the statement continued. “We are going to keep working around the clock to support our clients and make sure President Trump and his party enjoy a well-deserved beating at the ballot box.”

Incumbent Republican Senator Dan Sullivan is facing a midterm elections challenge from a former Democratic congresswoman, Mary Peltola, for a seat that could prove pivotal in determining which party controls the Senate.

One of the candidates in the race is also named Dan Sullivan, and Trump and officials in his administration have said the Democratic Party deliberately put the newcomer Sullivan up to running for office, to confuse voters on Election Day. Democrats have denied the accusations, and say that the ballots being used on Tuesday clearly mark each Sullivan separately.

But the Department of Justice, which unsuccessfully attempted to have a court block the certification of the election in the state if the incumbent Sullivan loses, has gone ahead with a sweeping investigation anyway.

The AP reported that more than 100 subpoenas had been sent out so far as part of the investigation, according to an unnamed person briefed on the probe.