The group was part of a 72-member contingent situated in two different locations in the area.
Those remaining are currently still under fire, preventing them from being moved out, the UN said in a statement issued from its New York headquarters.
"The UN Disengagement Observer Force (UNDOF) reports that, early this morning, UN Position 69 was fired upon by armed elements," the UN said in a statement issued from its New York headquarters.
The statement said another position was also attacked by "armed elements" with mortar and heavy machine gun fire and that the peacekeepers returned fire and prevented the attackers from entering.
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That position "is currently under fire, preventing the personnel from moving out," it added.
There are no reported casualties among UN personnel, the statement said.
However, "we are still working towards the safe release of the detained 44 Fijian peacekeepers," it added.
In Manila, Philippines Defense Minister Voltaire Gazmin said UN peacekeepers had clashed with Syrian rebels.
Gazmin said in an SMS statement to reporters that the Filipino troops had been "extricated" from one of their two positions but added that another group of Filipino soldiers "is now under attack."
The peacekeepers were besieged by rebels Thursday but defied demands that they give up their weapons.