Soon after the announcement, sirens wailed in parts of southern Israel alerting residents to a rocket attack.
The attack came less than an hour after Israel closed the crossing to the Egyptian resort and urged Israelis to leave "immediately".
The statement urged Israeli citizens in Sinai to leave immediately, emphasizing that the border would remain open to Israeli citizens returning to the country. One was an actual alert in response to a real rocket, while two were false alarms not triggered by ballistic launches.
The border closure appeared triggered by the bombing of Coptic churches on Sunday in the northern Egyptian cities of Tanta and Alexandria, killing at least 44 people and injuring more than 100.
Israeli Transportation and Intelligence Minister Yisrael Katz warned of a potential "terror attack" against tourists in Sinai in a statement Monday. Officials said that Israelis who were already in Egypt would be allowed to return through the border crossing. Israeli authorities are prohibiting citizens from entering the Sinai Peninsula.
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And I think that there will be a lot of answers that come out of that meeting", she told CNN's "State of the Union" on Sunday. But, she says it's not something the USA should do alone, explaining, "I don't think it's something for the U.S.to decide.
Joined the global condemnation of the church bombings in Egypt, US President Donald Trump said he is "so sad to hear of the terrorist attack" against the US ally. It also calls on Israelis planning trips to the Sinai to cancel.
The Prime Minister's Office announced the move in a statement that cited "the intensifying activities" of Islamic State-affiliated terrorists in the Sinai region in recent months.
It adds that with IS losing ground in Iraq and Syria, there is renewed "motivation to carry out terror attacks in different arenas at this time".
The Sinai Peninsula has been the site of ongoing violence between Egyptian forces and armed militant groups, which has increased since Egyptian President Abd al-Fattah al-Sisi took power from Muhammad Morsi of the Muslim Brotherhood, in 2013.
Egypt and Jordan are the only Arab countries that have signed a peace treaty with the Jewish state.