The prime minister's office said it had "concrete evidence" that terrorists were planning to attempt to kidnap Israelis in the peninsula.

Israel took the unusual step of calling on families of the Israelis who are visiting Sinai to contact them.

It fears that Palestinian militants will transfer hostages to Gaza through tunnels under the border.

The warning by Israel's security agencies came after a rumour that an Israeli had been kidnapped in Sinai. The Israeli emergency service Zaka later said that rumour was untrue.

"According to concrete intelligence, we anticipate an immediate terror activity to kidnap an Israeli in Sinai," Prime Minister Benjamin Netanyahu's office said on Tuesday.

Tens of thousands of Israelis routinely take holidays in Sinai over the Passover holiday. Most have returned after the week-long festival.

A few hundred were reported to have remained.

Egyptian police have been searching Sinai for any missing Israelis but found no evidence that anyone was missing.

Past attacks

In unusually strong wording, the Israeli anti-terror office called on "all Israelis residing in Sinai to leave immediately and return home".

Families of Israelis in the peninsula were urged to contact them and update them on the travel warning.

Israel's anti-terror office has a standing travel advisory telling Israelis to stay out of the Sinai desert because of the threat of terror attacks.

In 2004, suicide bombers attacked Egypt's Taba Hilton Hotel, just across the Israeli border, and several campsites popular with Israelis. Dozens of people were killed and hundreds wounded.

Israel controlled Sinai from its capture in the 1967 war until returning it to Egypt in 1982. The desert is just across the border, and its seaside resorts are popular with Israelis.

Sinai has been the scene of number of terrorist attacks, including bombings in the resort town of Sharm el-Sheikh in 2005 and Dahab in 2006, which killed dozens.