However, the Republic of Fiji Military Forces is checking the members of the civilian government named in the accord to see if they are still willing to serve in an administration appointed by the military.
Tarakinikini said Fiji, which has been without an effective government for five weeks, needed an administration to get the economy operating.
He met briefly with representatives of Speight's group to deliver the ultimatum, but neither Speight nor the ex-Army major in charge of the hostages, Ilisoni Ligairi, attended.
Tarakinikini said the military had told Speight the accord represented their last offer.
However, he said people should not expect an armed assault to free the hostages.
"We've given them 24 hours to come to a position and come back to us.
"A military option is always there, but it is not one we are intending to use.
"We believe it can be resolved peacefully."
The military is expected to step up pressure around the parliamentary complex where Speight is holding the hostages, enforcing checkpoints more vigorously and limiting food supplies.
Ironically, the Muanikau accord was a soft settlement for Speight's camp. It allowed Speight to nominate some members of an interim government, although the military would have the final say.
Speight's supporters would have been included on a committee to draw up a new constitution, which could ensure some political positions are held only by indigenous Fijians.
As well, a new president would have been free to include Speight or his team in Fiji's new cabinet.
If the deal is not agreed, Speight's camp loses all three options.
- NZPA
More Fiji coup coverage
Main players in the Fiji coup
The hostages
Under seige: map of the Parliament complex
Fiji facts and figures
Images of the coup - a daily record
George Speight: "I think I’m very sane. I’m certainly not mad."
