"There is absolutely no question of me resigning ... or of my government stepping down," Laisenia Qarase said on Wednesday in an address to the nation on local radio.
"We have the constitutional authority and the support of the people to rule now and for the next five years."
Military chief Frank Bainimarama has threatened to force Qarase to resign unless he drops two contentious bills, including one offering amnesty to some of those involved in a coup in 2000.
Bainimarama has accused the Qarase government of being soft on those involved and said that while the coup leader, failed businessman George Speight, was in prison those who backed him were now in parliament.
He said he regretted appointing Qarase as interim prime minister following the coup. Qarase has since won two free elections.
The military plans a march by 3,000 reservists through the streets of Suva on Thursday, a day after Fijian soldiers drove through the streets of Suva and took control of tonnes of ammunition from the waterfront.
Fijian political leaders failed to remove Bainimarama from his position on Tuesday, with the military rallying around him.
"Bainimarama is still commander and now the government is in a dilemma and will have to eat their words," commander Colonel Pita Driti told Fiji media on Wednesday.
Indigenous Fijians fear losing
power to ethnic Indian Fijians
Bainimarama, currently visiting troops in the Middle East, said he would remove Qarase from office once he returned to Fiji, saying the government was corrupt.
"I'll be back to see that Qarase and his cronies step down," he told the Fiji Sun newspaper on Wednesday. He is expected back in Fiji later this week.
Qarase said police were investigating Bainimarama's threats. "The rule of law must prevail. No one is above the law, no one has the right to interfere with the legal process."
Fiji has suffered three coups and a failed mutiny since 1987.
The coups have been racially fuelled, with indigenous Fijians fearful of losing political control of their island nation to ethnic Indian Fijians, who dominate the economy.
Australia has placed two warships on standby to evacuate its citizens.
"We are very concerned about the possibility of a coup in Fiji," Alexander Downer, Australia's foreign minister, told Australian Broadcasting Corp radio.
The US said it could suspend aid if troops do not respect constitutional processes and the rule of law.