(CNN) Sen. Bill Nelson's campaign and the Democratic Party's Senate campaign arm sued in federal court on Tuesday to lift the deadlines on the statewide recount taking place in Florida, arguing that they are "arbitrary" and "impose a severe burden ... on the right to vote."

If successful, the suit would "extend the deadline for recounting of all the votes statewide in the US Senate race," the campaign said in a statement.

"The lawsuit seeks to allow all local elections officials in the 67 Florida counties the time they say is needed to finish a legally mandated and accurate recount because the race was so close," the campaign said of the suit, which was filed in the US District Court for the Northern District of Florida.

Lawyers for the Democrats argued that the current deadlines -- November 15 by 3 p.m. for machine recounts and November 18 by noon for the hand recounts -- "will result in the disenfranchisement of voters who associate with Plaintiffs, and this serious and immediate harm warrants the issuance of a declaratory judgment."

The new filing -- which comes on top of four earlier lawsuits that are making their way through the legal system -- are the latest salvo in the Democratic effort to ensure through court action that a variety of ballots in question are counted in the three statewide races. Both Nelson, whose efforts have been steered by lawyer Marc Elias, and the campaign of his opponent, Republican Gov. Rick Scott, are increasingly turning to the courts in an effort to shape a broader fight over the scope of the count and, eventually, final recount.

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