Fiji army chief Mosese Tikoitoga said the rebels wanted their organisation, the Al-Qaeda affiliate Al-Nusra Front, to be removed from the UN's list of terrorist organisations.
He said they also wanted humanitarian aid sent to a small town which is an Al-Nusra stronghold just outside Damascus and were demanding compensation for three of their fighters who had been hurt in recent days.
"These are the official demands that are being quoted to the UN for the release of our boys," Tikoitoga told reporters in Suva.
Tikoitoga said there were 45 troops in the captured peacekeeping deployment, not 44 or 43 as authorities originally stated. He released the names of the soldiers and said the Fiji government was operating a crisis centre for their families in Suva.
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He said a UN negotiation team had arrived in the Golan Heights from New York to take over negotiations with the rebels.
"But they continue to reassure us that they're being well looked after, they're being fed well and are being kept safe. They've also told us that they've been taken out of battle (combat) areas."
The Fijians were captured last Wednesday when the rebels stormed a Golan Heights crossing.
Another group of 72 Philippine peacekeepers refused to surrender and eventually escaped from two camps on the Syrian side of the border after the rebels besieged them.