Sami Abu Zuhri, a Hamas official, said Israel and the US were pressuring Egypt not to allow the pilgrims to return to Gaza.
Abu Zuhri said: "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 officials said that 2,200 Gaza pilgrims were stranded on the ships and said a 62-year-old woman had died aboard one of the ships after falling ill.
The group fears Israel will arrest some of the pilgrims, who Israel believe may be carrying money for Hamas and other groups.
Hussein Abdul Ghani, Al Jazeera's Cairo bureau chief, said the Egyptian authorities were considering three options:
The first to receive assurances from Israel to let the Palestinian pilgrims return to Gaza via Israel without arresting any of them.
The second option to move the pilgrims to camps near Arish, in the Sinai region of Egypt.
The third was to let the pilgrims return through the Rafah crossing, against the wish of the Israeli government.
Israel had protested against Egypt's decision to let the pilgrims leave the Gaza Strip through the Rafah crossing to perform the Hajj earlier in the month.
But Ahmed Abdul Gheit, Egypt's foreign minister, said that he was "not concerned" about the Israeli protests; what concerned him was enabling Palestinian pilgrims to perform the Hajj, he said.
Earlier, a Jordanian foreign ministry official said in the capital, Amman, that the pilgrims sailed from Aqaba to Nuweiba after a promise that they could re-enter Gaza from Rafah.
|Egypt has considered placing the pilgrims in a |
refugee camp in the Sinai temporarily
"The foreign ministry contacted the Egyptian authorities and secured permission for the Palestinian pilgrims to go back to Gaza via Rafah," Jordan's state-run Petra news agency quoted the official as saying.
According to Petra, the pilgrims refused to go back to Gaza through the Israeli-controlled Karm Salem crossing "because many of them are relatives or families of martyrs and other people are wanted by Israeli authorities".
About 7,000 people waving Palestinian and Hamas flags gathered on the Gaza side of the border with Egypt on Saturday and demanded the pilgrims be allowed to enter.
"We won't accept any excuse for preventing the pilgrims from returning," read a banner carried by one of the protesters.
About 100 Egyptian riot police mounted a machine gun on a building overlooking the corridor separating Egypt from Gaza.
Hamas security positioned themselves between the protesters and the border gate, and the crowd eventually dispersed.