The two men, Abdulla Merhi, 20, of Fawkner, and Hany Taha, 31, of Hadfield, were among 18 people arrested in Sydney and Melbourne in a series of raids in November.
Magistrate Reg Marron said the pair did not meet the exceptional circumstances required for a bail application in this case.
Prosecutors also alleged they discussed launching a holy war, in telephone conversations secretly taped by police.
Prosecutor Nick Robinson said police intercepted discussions between the alleged leader of the group, Muslim preacher Abdul Benbrika, and Merhi.
Robinson told the court that in the conversation Merhi said: "For example if (Prime Minister) John Howard kills innocent Muslim families do we ... do we have to kill him and his family ... his people like at the football?"
Benbrika allegedly replied: "If they kill our kids we kill little kids".
Merhi then said: "Innocent ones" and Benbrika replied "innocent ones," according to transcripts of the discussions read out in court.
Mr Howard is a staunch ally of US President George W Bush's so-called war on terrorism, and Australian troop contingents have been sent to both Afghanistan and Iraq.
Merhi and Taha on Wednesday swore on the Koran that they would obey bail conditions if they were released.
When Merhi was asked what would happen if he lied in an oath on the Koran, he said: "I would have to live with the fear of entering hell".
Magistrate Marron said while the prosecution's case against the pair was "not overwhelming", the recorded conversations showed "disturbingly strong and reasonably assertive positions".
In refusing bail, Mr Marron also expressed some concern at the conditions in which the two men were being held at the maximum security Acacia Unit at Barwon Prison.
Merhi and Taha are among 10 men charged last month with belonging to a terrorist organisation,
Eight of the men have also been charged with financing a terrorist organisation,
The alleged leader of the group, Muslim preacher Benbrika, 45, of Dallas, has also been charged with directing a terrorist organisation.