The Forum for Law in Israel and two residents of the Ulpana outpost Sunday requested the court to halt its earlier order to evacuate the settlement, The Jerusalem Post reported.
They also asked the court to freeze any plans to destroy or evacuate the structures pending a decision by the Jerusalem District Court on whether the Jewish Ulpana's current residents acquired their land rights legally.
The petitioners say the High Court went outside its jurisdiction when it ordered the eviction while the district court matter had not been settled yet.
The case in the district court is not expected to be resolved in the near future, making a decision to delay the evacuation until that case is resolved effectively an indefinite delay.
However, the High Court and the government have maintained that the outpost was illegal for years.