A meeting of the security cabinet late on Thursday approved immediate steps to increase humanitarian aid to the civilian population in the Gaza Strip.
Andres said the World Central Kitchen (WCK) charity group he founded had clear communication with the Israeli military, which he said knew his aid workers' movements.
Seaborne aid for the population of Gaza is returning to Cyprus following the killing of seven aid workers of World Central Kitchen, Cypriot officials said on Tuesday.
Lt. Col. Richard Hecht said that the IDF would continue to facilitate humanitarian aid to Palestinian civilians, who he said were taken captive by Hamas.
In his visit, Gallant warned that "those who think we are delaying [the invasion of Rafah] will soon see that there is no place we cannot reach."
Michael Fakhri claimed US aid to Gaza is a "performance."
Prime Minister Benjamin Netanyahu had reportedly postponed a decision on the issue, with civil order increasingly strained in Hamas-run Gaza.
Under the arrangement, cargo would undergo security inspections on Cyprus, by a team including Israeli officials.
The Fact Finding and Assessment Mechanism (FFAM) is expected to conduct an independent investigation.
A convoy of trucks started making its way towards Gaza City, but struggled to make progress as hungry crowds tried to attack the trucks, which then faced gunfire as they entered the city.