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Former President Donald Trump's legal team has filed its written response to Special Counsel Jack Smith's request that the U.S. Supreme Court hear Trump’s immunity claims in the election interference criminal case against him. 

In their brief, the Trump team urged the high court not to rush things and accept the issue before the lower courts have heard the matter.

"This appeal presents momentous, historic questions," the brief states. "An erroneous denial of a claim of presidential immunity from criminal prosecution unquestionably warrants this Court’s review. The Special Counsel contends that ‘[i]t is of imperative public importance that respondent’s claims of immunity be resolved by this Court.’

"That does not entail, however, that the Court should take the case before the lower courts complete their review. Every jurisdictional and prudential consideration calls for this Court to allow the appeal to proceed first in the D.C. Court."

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Donald Trump and Jack Smith

Special Counsel Jack Smith, right, is asking the U.S. Supreme Court to hear former President Donald Trump's immunity claims in the election interference criminal case against him. (Getty Images)

Smith is expected to file a final written rebuttal in the next few days to urge the court to quickly accept the case on its merits. The justices will then privately consider whether to review the case. 

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Smith has made his request for the high court to act quickly to prevent any delays that could push back Trump's trial until after next year's presidential election. 

Supreme Court building

The U.S. Supreme Court in Washington, D.C., on Feb. 28. (Valerie Plesch/Bloomberg via Getty Images)

A federal judge previously ruled the case could go forward, but Trump said he would ask the federal appeals court in Washington to reverse that outcome. Smith is attempting to bypass the appeals court — the usual next step in the process — and have the Supreme Court take up the matter directly.

"This case presents a fundamental question at the heart of our democracy: whether a former President is absolutely immune from federal prosecution for crimes committed while in office or is constitutionally protected from federal prosecution when he has been impeached but not convicted before the criminal proceedings begin," prosecutors wrote.

Trump faces charges accusing him of working to overturn the results of the 2020 election in which he lost to President Biden before the violent Jan. 6, 2021, protest by his supporters at the U.S. Capitol. He has denied any wrongdoing.

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Should the justices decline to step in, Trump's appeal would continue at the U.S. Court of Appeals for the District of Columbia Circuit. Smith has asked for quick review there, too, but said even a rapid appellate decision might not get to the Supreme Court in time for review and final word before the court's traditional summer break.

Fox News Digital's Bradford Betz contributed to this report.