An assistant minister in the prime minister's office, Adi Ema Tagicakibau, was allowed out of the parliament building to attend her sister's funeral on the understanding she return afterwards.
Speculation is growing in the capital Suva that Prime Minister Mahendra Chaudhry and other hostages will soon be released.
But international condemnation is growing, with Commonwealth foreign ministers due to meet in London next week to discuss their response to the crisis.
Australia has condemned a decision by Fiji's military rulers to offer an amnesty to Mr Speight as unacceptable.
Australian Foreign Minister Alexander Downer said Mr Speight was "a terrorist... who has put a gun to the head of the prime minister of the country".
New Zealand Prime Minister Helen Clark said that only the fact that hostages were being held was delaying measures against Fiji, which would be "inevitable" upon their release.
Free
Fiji's military leader Frank Bainimarama - who took power on Monday in an apparent attempt to end the crisis - told the BBC that he would honour an amnesty offer made by President Ratu Sir Kamisese Mara.
When asked if that meant that Mr Speight would go free when the current stand-off is resolved, Commodore Bainimarama said: "Yes, I am sorry to say that."
Commodore Bainimarama said Mr Speight now had the three things he said he wanted before releasing his hostages: the ousting of the president, an amnesty, and the removal of the constitution.
"We have done all we can to facilitate the release of the hostages," he said.
"We have granted all three of their requests. I really don't know what else we can come up with, what other agenda is on their plate."
New PM
Commodore Bainimarama has named Ratu Epeli Nailatikau as interim prime minister.
Ratu Nailatikau's wife, Adi Nailatikau Mara, is among the 30 hostages being held in parliament.
She is also the daughter of President Ratu Mara.
Ratu Nailatikau was Fiji's army commander until he was overthrown in an earlier military coup in 1987 and later became Fiji's high commissioner to the UK.
Journalists outside the parliament complex said Mr Speight's supporters were rejecting Ratu Nailatikau's appointment and threatening people, including an ethnic Indian taxi driver whose taxi they hijacked.
Mr Speight, who declared himself prime minister early in the hostage drama, has so far refused to recognise the authority of Commodore Bainimarama.
He says the military leader remains loyal to President Ratu Mara, who is now reported to be staying on a boat in Suva harbour for his own safety.
Constiution
On Tuesday, the military scrapped the multi-ethnic constitution adopted in 1997, which had allowed the first ethnic Indian prime minister to take power.
The 1990 constitution, which has now been revived, reserves specific ministerial portfolios for ethnic Fijians, including the prime minister.
As the crisis continues, Commonwealth leaders have announced that they will meet next week in the first step towards calling for Fiji's suspension from the organisation's meeting.
The Indian Government has announced it is sending an official, S T Devare, to Australia and New Zealand to discuss the situation.
Some 44% of the population in Fiji are ethnic Indians, who first came to the islands in the 19th century to work in sugar plantations.
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