Egypt's military has pledged to hunt down those behind the killing of its 16 soldiers at a checkpoint along the Sinai border with Israel.
It described on Monday the attackers as "enemies of the nation" who must be dealt with by force and suggested they were Sinai-based Egyptian fighters who received Palestinian support from the Gaza Strip.
Security and military officials said at least two helicopter gunships arrived in the border town of El-Arish on Monday to join the hunt.
Israel, meanwhile, stepped up pressure on Egypt to clamp down on the lawless border region.
Israel says its aircraft killed eight fighters who broke through the border after the killings.
Egyptian officials have said six attackers were killed.
A statement by the Egyptian armed forces said 35 armed fighters took part in the attack, suggesting that close to 30 of them may be on the run.
No group has yet claimed responsibility for the attack.
Egypt and Israel say both Islamist fighters from the Sinai and Palestinian allies from the Gaza Strip are active in northern Sinai, attacking both Egyptian security forces and staging raids across the border into Israel.
The Egyptian armed forces' statement suggested that groups on both sides of the border may have been involved.
"The armed forces have been careful in the past months and during the events of the [Egyptian] revolution [in 2011] not to shed Egyptian blood ... but the group that staged yesterday's attack is considered by the armed forces as enemies of the nation who must be dealt with by force," it said.
In the first direct indication that the attackers may have had the help of Palestinian fighters, the military's statement said "elements from the Gaza Strip" aided the attackers by shelling the Egyptian-Israeli border crossing of Karam Abu Salem with mortars as the attack was taking place.
Earlier on Monday, Mohamed Morsi, the Egyptian president, pledged that he will retake control of the Sinai.
"I have given clear orders to all of our security forces, the armed forces as well as the interior police, to move swiftly in capturing those behind this vicious attack," he said in a television address early on Monday.
"This incident will not go lightly. The security forces will implement entire control over all of these areas within Sinai and will ensure they are controlling it. Those behind the attacks will pay a high price as well as those who have been co-operating with those attackers, be it those inside or anywhere in Egypt."
A senior security official, speaking on condition of anonymity because he was not allowed to speak to reporters, said seven other guards were wounded in the attack.
He said the attackers seized an armoured vehicle before driving away.
Israel said the attackers commandeered two Egyptian vehicles and tried to storm its border.
One of the vehicles exploded and the second was targeted by Israeli aircraft, Avital Leibovich, a military spokeswoman, said.
Ehud Barak, Israel's defence minister, said that eight of the attackers had been killed. He said the raid showed need for "determined Egyptian action" to impose security and "prevent terror in Sinai".
Brigadier-General Yoav Mordechai, an Israeli military spokesperson, said on Monday that intelligence services had received reports of a planned attack beforehand and were "prepared for it".
Akiva Eldar, the chief political correspondent for the Israeli daily Haaretz, said, "The Israelis are in a way quite happy that the Egyptians have learnt their lesson, that they have to listen to us, and have had to pay the price," with Egpytian president Morsi having to work with the Israeli authorities to ensure this does not happen again, he said.
"The message from the Israelis is that 'we cannot trust anyone....we cannot afford to give away the responsibility of the security of our people to anyone'," said Eldar.
There is increased security along the border area following the attack. "The entire border area has been sealed with very heavy security on all the roads leading up to Sinai and not just the border area," Al Jazeera's Rawya Rageh said.
In a statement, Hamas, the Palestinian group controlling Gaza, condemned the attack, calling it an "ugly crime" and extended "deep condolences to the families of the victims and to the leadership and the people of Egypt".
Lucrative tourist income
Taher al-Nono, a Hamas spokesperson, said that the group was temporarily closing all tunnels along the border with Egypt immediately.
The Sinai is home to Egypt's Red Sea resorts, a source of lucrative tourist income, and is also where the country's Bedouin, who were long marginalised under the rule of fallen president Hosni Mubarak, are based.
Before the July attack in Sheikh Zuwaid, a town roughly 15km west of the Gaza Strip, the fighters had distributed pamphlets calling on the army, brought in to restore security, to leave the lawless north of the peninsula.
The military sent tanks and soldiers into the region last year to quell Islamist fighters, after receiving permission from Israel.
Under a 1979 peace treaty with Israel, Egypt should have a limited military presence in the area.
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