He said there was now no reason for the gunmen inside parliament to continue holding members of the civilian government hostage.
The president again offered coup leader George Speight a pardon.
But the peace offer was quickly rejected by a spokesman for the coup plotters.
In a complicated constitutional manoeuvre on Saturday, President Mara appointed a caretaker administration, which then immediately resigned, leaving him as Fiji's sole authority.
Parliament would be suspended for the next six months, the president told a news conference.
Shots fired
Earlier, shooting broken out between government troops and the rebels who are holding more than 30 hostages, including ethnic Indian Prime Minister Majendra Chaudry.
A press cameraman was wounded in the arm and a government soldier was also reportedly injured.
Government soldiers opened fire when about 200 supporters of the rebels left the compound to try to overrun an army barricade which was preventing others trying to join those inside the parliament.
But a senior military officer has ruled out armed intervention because of fears for the safety of the hostages.
Fiji condemned
In the capital, Suva, the police say they are cracking down on people breaking the night-time curfew. Thirty-eight were arrested on Friday night and face up to two years in jail.
The rebels two days ago were given some support by Fiji's Great Council of Chiefs, who have called for Mr Chaudhry to be replaced by an interim government and for a pardon for the rebels.
Amid continuing international condemnation of the coup, Australian Foreign Minister Alexander Downer said Fiji should be suspended from the Commonwealth.
Canberra is also considering a range of economic, political and military sanctions.
The coup has also been strongly condemned by the United Nations, Commonwealth and countries including the United States, Britain, and Australia.
Mr Downer denounced coup leader George Speight as a "terrorist" and called on the country's Great Council of Chiefs to resist caving in to his demands.
"If Speight and his gunmen are successful then this will be an international disaster for Fiji," he added.
Australia told Fiji that an unconstitutional resolution of the crisis could lead to the suspension of aid from its major donors, and the US warned of sanctions.
'Pacific Apartheid'
The coup leaders want a constitution ensuring the country can only be ruled by indigenous Fijians.
But Mr Downer described the situation in Fiji as "Pacific apartheid".
Commonwealth Secretary-General Don McKinnon added: "Aiming a loaded gun at the constitution to marginalise sectors of Fiji's society is totally unacceptable.
"This is a major step backwards for Fiji as we start a new millennium."
Mr McKinnon, who met Mr Speight in Fiji this week, has convened a meeting of Commonwealth members to discuss the crisis.