They were also told they would be forcibly taken to the Queen Elizabeth Barracks if they refused any summons.
In issuing the warning, Major Neumi Leweni, a spokesman for the military said: "The military wants this transition to be smooth".
Several prominent Fijians have already been taken to the capital's barracks and been ordered not to make further comments, while Fiji's human rights commission said it was investigating reports of "inhumane treatment" of one person detained.
Opposition to the coup is said to be growing and, the country's churches have already called it illegal.
Bainimarama claimed the government was corrupt and soft on those behind the last coup, in 2000. Fiji has had four coups since 1987.
The military even took out advertisements in the Fiji Times newspaper on Saturday seeking people of "outstanding character" to fill cabinet posts in an interim government.
|"The military wants this transition to be smooth"|
Fijian military spokesman
Meanwhile Qarase told the Australian Associated Press from his home: "I have been in touch with my parliamentary colleagues and other key people and we will get together to assess the situation and what can be done next to peacefully restore democracy."
"If Bainimarama is in a tight corner, he might see his way clear to pull back," he said.
The coup has brought international condemnation, with Australia, New Zealand, Britain and the United States imposing economic and defence sanctions.
A former British colony, Fiji had its Commonwealth membership suspended overnight in protest at the coup. Fiji was also suspended from the Commonwealth after the coups in 2000 and 1987.