Al-Jazeera English says Australian correspondent Peter Greste, Egyptian-Canadian acting bureau chief Mohammed Fahmy and Egyptian producer Baher Mohamed were only doing their jobs before they were taken into custody on December 29.
They have been held at Tora Prison, and have been interrogated on suspicion of having unlicensed equipment and broadcasting false news that harmed national security.
Greste's parents, Lois and Juris, held a news conference in the Australian east coast city of Brisbane in which they called for their son's release.
"We wish the Egyptian people peace and prosperity. However, Peter's detention is most unfair and unjustifiable," he said. "Thus we respectfully but passionately ask the Egyptian prosecutor to free Peter and his colleagues immediately."
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Peter Greste is an award-winning journalist who has worked for Australian Broadcasting Corporation, Reuters, CNN and BBC.
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.
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.