"The State of Israel should make it easier [for Palestinians] to cross [from Gaza to the West Bank]," Justice Minister Daniel Friedmann said Monday morning, "so long as those crossing are not Hamas members or persons endangering [Israel's] security."
Also Monday, Israel began passing medical equipment to Gaza through the Erez Crossing, Israel Radio reported.
The equipment was transferred to Gaza with the help of the Red Cross organization.
On Sunday, some 300 Palestinians gathered at Erez Crossing in an attempt to escape the Hamas-controlled Gaza Strip into Israel.
In a similar incident on Saturday, IDF soldiers shot into the air to try to prevent the approaching crowds from infiltrating through the security fence.
Israel said that only a small number of "humanitarian cases" were being allowed to pass.
One family was allowed to enter Israel Sunday morning.