On Monday, the border authority said that no one who was not on one of the lists would be allowed through, citing Egyptian authorities.
At least 320 foreign nationals and dozens of severely injured Gazans were among the first beneficiaries of the Qatari-mediated deal brokered between Egypt, Israel and Hamas.
"As long as we have a degree of certainty that some of the aid is being diverted to Hamas - and we do have that certainty - then all the states of the world must refrain from providing [it]."
Israel imposed a total blockade and launched air strikes on Gaza in response to a deadly attack on Israeli soil by Palestinian group Hamas on Oct. 7.
Israel's bombardment and siege of Gaza is in retaliation for a devastating Hamas incursion into Israel on Oct. 7 during which 1,400 people were killed and hostages were taken.