Some 100 to 200 Palestinians are now waiting at Erez Crossing for the chance to flee the Hamas-controlled Gaza Strip.
However, Israeli army closed the crossing for fear of infiltration of Palestinian territories along with the fled Palestinian civilians.
On Monday evening, a gunmen opened fire at those Palestinians waiting for permission to enter Israel near Erez Crossing, killing one and injured around 15 others.
Under humanitarian considerations, Barak instructed officials to let in an unspecified number of Palestinians for medical treatment.
Gaza now is on the grip of the Islamic Resistance Movement ( Hamas) after it defeated its rival Fatah movement led by Palestinian President Mahmoud Abbas and seized all Fatah positions in Gaza.
In the wake of the Hamas' violent takeover of the Gaza Strip, Abbas sacked the unity government led by Hamas and swore in an emergency government in the West Bank city of Ramallah.
The United States and the European Union have expressed support to the emergency government and vowed to lift the embargo on the West Bank while the Gaza was still under strict Israeli blockade.