The parents of Al Jazeera correspondent Peter Greste have appealed for their son's release from an Egyptian prison, saying the accusations levied against him are preposterous.

Greste along with acting bureau chief Mohamed Fahmy and Egyptian producer Baher Mohamed have been held at Tora prison since December 29 on suspicion of having unlicensed equipment and broadcasting 'false news' that harmed national security.

Lois and Juris Greste told a news conference in Australia that their son was just doing his job.

"To think or allege that Peter or his high-achieving colleagues would jeopardize their mid-life international careers by unethical or improper practices is completely preposterous," Juris Greste said.

"We wish the Egyptian people peace and prosperity. However, Peter's detention is most unfair and unjustifiable.

"Thus we respectfully but passionately ask the Egyptian prosecutor to free Peter and his colleagues immediately," he added.

Peter Greste is an award-winning journalist who has been a foreign correspondent since 1991, working for Australian Broadcasting Corp., Reuters, CNN, BBC and Al Jazeera.

Lois Greste praised the efforts of Australia's Foreign Department. She said she had received a 20-minutes phone call from Australian Foreign Minister Julie Bishop on the issue.

"There's no charge laid. All of the... allegations are quite ludicrous really, because we know that Peter -he's a veteran journalist, foreign correspondent who goes in and out of countries consistently - he was only doing his job," she told ABC.

She said her son had been kept in solitary confinement for his first 15 days in custody. He was now allowed out of his cell for four hours a day to exercise and to mix with his fellow inmates, she said.

International journalists and an Egyptian journalists' union have also called on the Egyptian government to release Peter and the Al Jazeera team.

Signed by senior representatives from CNN, the Associated Press, the Observer, the Washington Post, Le Monde, the Daily Telegraph and others, the statement called for their release and that of other journalists, some of whom had been imprisoned for more than five months.

Al Jazeera Arabic's Abdullah Al Shami and Al Jazeera Mubashar Misr cameraman Mohammed Badr also remain in custody having been held since July 2013.