Austria announced it would pull out its 377 peacekeepers from the 911-member UN force after fighting from the Syrian civil war threatened their positions last week.
The first contingent, of between 60 and 80 troops, left on Wednesday and Austria had said the withdrawal would be complete in two to four weeks.
UN spokesman Martin Nesirky said the peacekeeping department "has requested the Austrian authorities to ensure that the withdrawal of its personnel takes place in an organized manner, taking into account the mission's operational requirements and the possible negative impact on implementing the mandate."
Austria's UN Ambassador Martin Sajdik told AP: "This request is known to us and the responsible authorities in Vienna and people are working on this request."
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The UN force was established in 1974 to monitor the disengagement of Israeli and Syrian forces in the Golan Heights following intensified firing on the Israel-Syria border after the 1973 Arab-Israeli war.
In recent months, Syrian mortars overshooting their target have repeatedly hit the Israeli-controlled Golan, and Israel has responded on several occasions.
Rebels have also abducted three groups of UNDOF peacekeepers since March. All were released unharmed after negotiations.
Austria's withdrawal deals a heavy blow to the UN forces, leaving just 341 Philippine soldiers and 193 from India.
Croatia withdrew in March, fearing its troops would be targeted. UN diplomats, speaking on condition of anonymity because no announcement has been made, said the Croatian contingent is expected to be replaced by Fijian troops.