Former US President Donald Trump has appealed a court order asking Mike Pence, his vice president during the US presidency, to testify in a special investigator's investigation into efforts to overturn the results of the 2020 presidential election, a source familiar with the matter said.

Trump's lawyers filed the appeal following a ruling related to the Justice Department's investigation into efforts to undermine the 2020 presidential election, which Republican Trump lost to Democrat Joe Biden.

The case remains unavailable, and several of Trump's lawyers did not immediately respond to a request for comment.

Final submissions on appeal are due to be filed by 25 May, according to the court's preliminary timetable and the parties to the case have not been named.

Pence said last week he would not appeal a judge's ruling requiring him to testify before a federal grand jury about his conversations with Trump before the deadly attack on the Capitol on Jan. 6, 2021.

In a March ruling, the judge also said Pence could still refrain from answering questions about Jan. 6.

Special counsel Jack Smith, appointed by Attorney General Merrick Garland in November, is investigating Trump.

One of the two investigations overseen by Smith is looking at attempts to interfere with the peaceful transition of power after Trump's November 2020 loss to Biden, while the second is looking at Trump's keeping of classified documents at his Mar-a-Lago resort in Florida after leaving office in January 2021, and his possible attempt to obstruct the Justice Department investigation.