Israel took the decision to reopen the crossings as rocket and mortar attacks launched at southern Israel stopped since an attack on Thursday in defiance of a truce that took effect June 19.
Several rockets and mortar rounds have been fired at Israel from Gaza since the truce between Israel and the Hamas began.
The ceasefire was supposed to lead to the easing of the crippling blockade Israel imposed more than a year ago when the Hamas seized power in Gaza.
Prisoner swap talks
Hamas on Friday said it was suspending talks over the release of Gilad Shalit, an Israeli soldier captured in a deadly cross-border raid in June 2006, because of the closures, which it said was a violation of the Egyptian-brokered truce.
Israel’s Maariv newspaper reported on Sunday that security officials hoped the reopening of the crossings would encourage Hamas to renew negotiations aimed at a prisoner swap for Shalit.
Hamas has demanded the release of 1,000 Palestinian prisoners jailed by Israel in exchange for Shalit, including about 450 people serving long sentences.
The proposed list includes the names of several Palestinian fighters convicted of carrying out deadly attacks on Israelis.
Hamas has meanwhile insisted that its own fighters are respecting the truce and has vowed to arrest anyone who violates it.