"I will certainly try my best to be in power for the next 4 and a half years," Qarase, who was re-elected in May to a second five-year term, said.
Qarase and Bainimarama, who has also had discussions with Madraiwiwi, have argued over whether Friday's deadline has now been extended.
"I am the one that will set the deadline not him, or maybe he wants to be the commander," Bainimarama said.
Qarase told Fiji radio that he was not considering a dissolution of parliament and hoped for direct talks with Bainimarama.
"There will be a fair bit of consultations continuing through the weekend and early next week, I hope"
Laisenia Qarase, Prime Minister of Fiji
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"There will be a fair bit of consultations continuing through the weekend and early next week, I hope. It is all about trying to resolve the differences that now confront our country."
But his rival said that the military was planning a peaceful transition to an interim government.
Bainimarama has repeatedly threatened to remove Qarase's government unless it drops three pieces of legislation, including a bill that would grant amnesty to those involved in a 2000 coup.
The prime minister has bowed to most of Bainimarama's demands, including suspending the three bills, but Bainimarama is still not happy.
He has accused Qarase of having people associated with the 2000 coup by armed indigenous nationalists in his government and high public offices.
Fiji has suffered three coups and a bloody but unsuccessful mutiny, during which Bainimarama was almost killed, since 1987.