The new truce won the praise of United Nations Secretary General Ban Ki-moon who, in a statement, urged both sides to "avoid any steps which would lead to a return to violence."
Ban expressed a "strong hope" the truce might lead to a "durable cease-fire for the benefit of all civilian populations and as a starting point to address the underlying grievances on both sides."
Hamas has demanded an end to Israeli and Egyptian blockades of the coastal territory and the opening of a Gaza seaport - a project Israel says should be dealt with only in any future talks on a permanent peace deal with the Palestinians.
Israel opened the Kerem Shalom crossing to bring goods into Gaza on Monday after having closed it down on Sunday due to rocket fire.
Herb Keinon contributed to this report.