Haneef, 27, was being detained in Australia under counterterrorism laws that allow police to hold a suspect without charge as long as a judge agrees there are grounds to do so, Australian Federal Police Commissioner Mick Keelty said.
No charges were filed Tuesday, and Keelty stressed it had yet to determine what role - if any - Haneef had in the plots. Officials did not say where he was bound when he was detained.
"There is suspicion, there is a complex investigation under way" Keelty said. "But we should be cautious here. Dr. Haneef may have done nothing wrong, and may at the end of the day be free to go."
"The doctor was regarded by the hospital as, in many senses, a model citizen - excellent references and so on," said Queensland Premier Peter Beattie.
A man arrested late Saturday on a highway in central England was also a physician, Mohammed Jamil Abdelqader Asha, police said. A Jordanian official said Asha was of Palestinian descent and carried a Jordanian passport.
Azmi Mahafzah, Asha's instructor at the University of Jordan medical school, said he knew Asha during his studies and training from 1998 to 2004.
"I didn't even have the impression that he was religious," he told The Associated Press. "He interacted with others, both boys and girls. He has no prejudices. He is not a fanatic type of person."
And police in Glasgow said two men arrested Sunday were aged 25 and 28 and detained at residences at the Royal Alexandra Hospital.
Officers would not confirm if the two men were also doctors, but Britain's Sky Television reported - without citing sources - that they were trainee physicians.
Associated Press Writer Dennis Passa contributed to this report in Brisbane, Australia.