The reason for their flight, during which three members of the tribe died from exhaustion, is disputed. The Bedouin say they are being persecuted by the Egyptian authorities because Bedouin on the Israeli side of the border belong to the Israeli army.
They also complain of food shortages and the lack of work in Egypt.
An Israeli army spokesman said that the real reason for their exodus is that several of the tribe had been killed in a blood feud with another Bedouin tribe in Egypt.
Another reason for the dispute may be rivalry over control of the lucrative drugs trade from Egypt into Israel, which is controlled by the Bedouin of the Sinai area.
The refugees are members of the Azazmeh tribe, which straddles the border. Although they are receiving food and medical attention from the Israeli army, they have not been allowed to pitch their tents. Tribal leaders say they will kill themselves rather than return to Egypt.
Their chances of gaining permanent residence in Israel do not look good. Avigdor Kahalani, the Public Security Minister, said: "It doesn't seem to me that the state of Israel will allow a situation where people simply migrate here."
Mr Kahalani said Israel needed to talk to the Egyptian authorities to decide what to do about the situation, which would be dealt with very soon.
The Bedouin started crossing the border on Sunday. "It's like the Exodus," Adva Loyd, from the local Negev regional council was quoted as saying.
The Foreign Minister, Ariel Sharon, said the Bedouin should be "sent back to the place from which they came". He added: "I don't think that any country in the world would permit people to suddenly cross its border and settle."
However, Israel's Supreme Court last night ordered the army not to forcibly remove the Bedouin from Israeli territory pending a court hearing on their request for asylum.
Embarrassed Egyptian officials visited the Bedouin in an attempt to persuade them to go back. Egypt said the matter was dispute between Bedouin and themselves and would not affect Egypt's ties with Israel.Reuse content