Lawyers for President Donald Trump's 2016 presidential campaign asked a judge Tuesday to penalize the Democratic National Committee for alleging in a lawsuit a conspiracy between the campaign and Russia, saying special counsel Robert Mueller's findings revealed the "doomed effort to prove a falsehood."

But lawyers for the Democratic Party responded by saying Mueller's report confirms and bolsters their claims by detailing the campaign's repeated suspicious interactions with Russian agents, proving the campaign participated in Russia's election interference.

The arguments on both sides were included in the Trump campaign's filing in Manhattan federal court, where a judge is considering the merits of the DNC's April 2018 lawsuit against the Trump campaign, Russia, WikiLeaks and Trump's son and son-in-law. The lawsuit sought unspecified damages, alleging a conspiracy to cheat Democrats.

In seeking sanctions Tuesday including legal costs, Donald J. Trump for President Inc. contended that Mueller "definitively refuted the notion that the Campaign conspired or in any way coordinated with Russia."

The 448-page Mueller report was released on April 18, though nearly 40% of the report's pages had redactions.

"The assumption, of course, was that the Special Counsel would substantiate the DNC's claims," the Trump campaign lawyers wrote. "Suffice it to say, that assumption did not pan out."

The campaign's lawyers said the report "debunks any such conclusion by walking through the vast body of evidence that his Office collected and establishing that none of this evidence showed that the Campaign formed any sort of agreement with Russia."

They said the report shows the DNC can never prove its key allegations, "yet has refused to accept this reality."

"The DNC has thus made clear that it wants to proceed with a politically motivated sham case, tying up the resources of this Court and the Campaign — and inevitably burdening the President himself — all in a doomed effort to prove a falsehood," the lawyers wrote.

The lawyers included exhibits with their filing showing that Trump campaign attorney Michael Carvin sent the DNC a May 13 letter demanding that it dismiss all of its claims against the campaign within three weeks or he'd seek sanctions.

On Sunday, DNC lawyer Joseph Sellers responded, saying any request for sanctions could be met by sanctions against the campaign.

"Over the course of more than 100 pages, the Report details the Campaign's repeated suspicious interactions with Russian agents, confirming and bolstering the central allegations of the DNC's" lawsuit, he said.

"The Special Counsel specifically warned that his 'statement that the investigation did not establish particular facts does not mean there was no evidence of those facts,'" Sellers said. "Indeed, he reiterated in a televised press conference last week that a decision not to prosecute should not be confused with an exoneration. And yet, this is exactly what the Trump Campaign does in its letter."

The DNC letter noted varying burdens of proof in civil and criminal cases and said fact-gathering tools available to civil plaintiffs like the DNC are not available to prosecutors like Mueller.