US prosecutors have appealed a lower court decision to dismiss allegations that former US President Donald Trump illegally retained classified documents.

The move comes after a Florida district judge last month dismissed the case accusing Trump of violating the Espionage Act. The judge said the appointment of Special Counsel Jack Smith was unconstitutional, as it had not been approved by Congress.

Smith filed a brief with an appeals court in Georgia on Monday, saying that Congress gives the Attorney General the authority to appoint special counsels. The brief said "the district court deviated from binding Supreme Court precedent."

US media reports say the special prosecutor has not asked for expedited treatment and that the legal process may take several months, possibly until after the presidential election in November.

Trump allegedly kept information, including highly classified documents about US nuclear programs and military capabilities, at his home in Florida in violation of the Espionage Act.