Many checkpoints, especially in the city of Arish, saw exchanges of fire. Egyptian security troops and helicopters were reported to be combing the eastern area of El-Halal Mountain, hunting for armed insurgents, according to state-run Ahram news website.

The attacks of three joint military-police checkpoints late on Tuesday night  in response to a deadly attack on Sunday on a police station, which left at least 16 Egyptian police officers have been killed and others wounded in north Sinai on the border between Egypt and Israel, authorities say.

Exchanges of fire lasted until the early hours of Wednesday before armoured vehicles were sent in an attempt to contain the situation, Al Ahram reported.

The northern parts of Sinai have sunk into a state of lawlessness since last year’s  uprising that ousted former president Hosni Mubarak.

No one has yet claimed responsibility of the terror attack.

The Muslim Brotherhood has blamed  Israel’s intelligence agency Mossad of carrying out the attack to “hinder Egypt’s progress.”

Hamas and Israel have both distanced themselves from the attack, which the latter’s defence minister Ehud Barak said hoped would serve as a “wake-up call” to Egypt, which has been struggling to assert control over the Sinai peninsula.

Egyptian president Mohamed Mursi declared three days of mourning for the slain border guards.  The Egyptian military strikes came a day after the military held a funeral for the 16 soldiers killed in Sunday’s attack.  Mursi did not attend the funeral, where some protesters chanted slogans against the Brotherhood and even heckled Prime Minister Hisham Qandil.

“The letter that the media reported to have been sent from President Mursi to Israel was fake. President Mursi has not sent anything to Israel,” spokesman Yasser Ali told Reuters.

An official from Peres’ office said the letter was authentic.

“It was received by the Egyptian ambassador and handed over (to Peres’s office). The denial was to be expected, given the letter’s high publicity in Israeli and Egyptian media,” the official said, speaking on condition of anonymity to Reuters due to the sensitivity of the issue.

Mursi reportedly told his Israeli counterpart in the letter that he wanted to work for peace in the Middle East.

In a copied image of the letter, obtained by AFP following its release by the office of the Israeli president, Mursi wrote that he planned to get the Middle East process “back to its right track.”

“I am looking forward to exerting our best efforts to get the Middle East peace process back to its right track in order to achieve security and stability for all peoples of the region, including (the) Israeli people,” Mursi said in the letter to Israeli President Shimon Peres.

Politicians in Israel had expressed concern in private over the election of the Muslim Brotherhood’s Mursi in June’s presidential vote as Egypt’s ousted President Hosni Mubarak had guaranteed the 1979 peace treaty with Israel for decades.

The Muslim Brotherhood is ideologically hostile to Israel and linked to Hamas which runs the Gaza Strip.