Bainimarama said the peacekeepers were believed to be safe and his government was working closely with the United Nations to secure their release.
"The latest information we have is that they are safe and I can say now that the negotiations for their release have already begun," he said in a statement.
"I want to assure the families of the soldiers we are doing everything possible to secure their safe return."
Bainimarama said Fiji was "united as a nation in praying for their safe return".
The Fijians, who were on duty in a UN patrolled zone, were taken hostage by about 150 Syrian rebels yesterday.
About 75 Philippine peacekeepers who refused to surrender were involved in a tense standoff with armed groups in the same area, Philippine officials said.
Israel seized 1,200 square kilometres of the Golan Heights during the 1967 Six-Day War, then annexed it in a move never recognised by the international community.
The UN peacekeeping force has been stationed there since 1974 to monitor a ceasefire between Israel and Syria. There are currently 1,200 peacekeepers from the Philippines, Fiji, India, Ireland, Nepal and the Netherlands.
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