Some 2,000 Palestinians returning from a pilgrimage to Mecca are stranded on two boats off the Egyptian coast.
The pilgrims are stranded off Nuweiba in the Red Sea
Egypt is insisting that they must re-enter Gaza through Aouja, a border crossing controlled by Israel.
The group is thought to include senior members of the militant organisation Hamas, and Israel believes some of them may attempt to smuggle funds into Gaza.
Hamas believes that if the pilgrims travel through Aouja, Israel will arrest the Hamas members.
Senior Hamas officials have accused Egypt of bowing to Israeli pressure by refusing to let the pilgrims cross into Gaza through the Rafah border crossing, which is the only entry-point into Gaza not controlled by Israel.
"We are aware of the Israeli and American pressures on Egypt, and we urge Egypt to reject these pressures and to allow the pilgrims a safe return through Rafah," Hamas official Sami Abu Zuhri told reporters.
No medical supplies
The pilgrims have been stuck for two days on two ferries at the Red Sea port of Nuweiba, where they arrived after participating in the annual Muslim pilgrimage, or Hajj, to Mecca, in Saudi Arabia.
Conditions on the ships are said to be worsening, with no medical supplies for those who have fallen ill.
In December, Israel allowed pilgrims to exit Gaza through Rafah
Since Hamas took control of the Gaza Strip in June 2007, Israel has increased its security cordon around the territory.
The Egyptian authorities agreed to restrict the Palestinian pilgrims' re-entry after a meeting with Israeli Defence Minister Ehud Barak, according to Israeli officials quoted by the Associated Press news agency.
In early December, Israel allowed some 2,200 Palestinian pilgrims to leave Gaza through the Rafah border-post.