The Egyptian army vowed on Monday to 'avenge' the killing of 16 guards by gunmen near the Israeli border, as President Mohamed Morsi ordered security forces to take full control of the increasingly lawless Sinai Peninsula on the frontier.

In Sunday's attack, gunmen in Bedouin attire drove up to a border post and opened fire before crossing into the Jewish state in an armoured vehicle, Egyptian officials said. Israel said five gunmen were killed on its side.

The 1979 peace treaty between Egypt and Israel, under which Israel withdrew from the Sinai, which it had occupied in the 1967 Middle East war, set strict limits on Egyptian troop numbers in the peninsula.

But Israel has complained of growing lawlessness on its southern border since the overthrow of veteran strongman Hosni Mubarak early last year and called for action by Cairo.

"We swear in the name of God to avenge them," the Egyptian army said in its statement on Monday.

"Egyptians will not have to wait long before they see a reaction to this attack by terrorists," it said in the statement carried by the official MENA news agency.

"Anyone liaising with these groups that have attacked our troops in the Sinai in recent months will pay dearly, be it inside Egypt or abroad," the Egyptian army said.

Israel said two armoured vehicles were seized, one of which exploded by itself and the other of which was destroyed by a helicopter.

"The bodies of the five gunmen have been found by the Israeli army," an Israeli military spokesman said, but did not give details.

The Israeli military's top spokesman, Yoav Mordechai, told army radio: "We were ready because we had previous information from Shin Bet (security service) and from military intelligence services, which allowed us to thwart a bloody attack."

The armoured vehicle that crossed the border "fired in every direction after entering Israeli territory before being attacked by tanks and from the air," Mordechai added.

He said the gunmen were 'members of the global jihad based in Sinai, which has become a hothouse for world terrorism because of the weak control exercised' by Egypt.

President Morsi said he had given 'clear instructions' that Egypt must take 'full control of the Sinai'.

Morsi, who only took the oath of office on June 30 to become Egypt's first freely elected leader and its first head of state since Mubarak's overthrow, said those who committed the "cowardly" attack and those who worked with them would pay dearly.

"Those responsible for this crime will be hunted down and arrested," he said.

"Everybody will see that the Egyptian military and police forces can get these criminals wherever they are," he said. "These criminal, these attackers do not belong among us."

Israel's former ambassador to Egypt, Yitzhak Levanon, said on Monday that the incident was an attack on "Egyptian institutions, as well as on President Mohamed Morsi, the army and the intelligence services."

The health ministry said after the attack that 16 soldiers and border guards had been killed, while a security official said another seven were wounded.

Egypt's MENA news agency said the gunmen were 'jihadists' who 'infiltrated from Gaza through tunnels in collaboration with jihadist elements in the Al-Mahdiya and Gabal Halal areas' inside Egypt.

They attacked a border post while the soldiers and officers were taking iftar, the meal that breaks the Ramadan fast, it added.

State television and MENA reported that Egypt was closing its Rafah frontier crossing with Gaza 'until further notice'.

Rafah is the only crossing between Gaza and the outside world that is not under Israeli control.

An Israeli military spokeswoman confirmed that the incident had taken place in the Kerem Shalom area.

"A few of the people who manned the vehicles started running away. We targeted them," she said.

Nearby Israeli communities were ordered to stay inside their homes until further notice, she added. No Israeli civilians or soldiers were wounded.

Big attack foiled

Israeli Prime Minister Benjamin Netanyahu hailed 'the determined action of the military' and Shin Bet in 'ensuring the failure of a large attack on Israeli civilians'.

Defence Minister Ehud Barak said: "The way these attackers acted again shows the need for the Egyptian authorities to act firmly to re-establish security and fight terrorism in the Sinai."

Gaza's Hamas rulers dismissed the the idea that militants from inside the territory may have been involved.

"We condemn this ugly crime in which Egyptian soldiers were killed, and send our condolences to the families of the victims, and to the Egyptian leadership and the Egyptian people," a statement said.

Sinai-based Islamist militants are believed to have been responsible for several rocket attacks against Israel.

Israel also accused them of having carried out a cross-border ambush last August that killed eight Israelis, and they have also been blamed for repeated bombings of a pipeline that exports gas to Israel and Jordan.

The Sinai is home to Egypt's Red Sea resorts, a source of lucrative tourist income, and is also where the country's Bedouin, long marginalised under the Mubarak regime, are based.

To stop any attacks and illegal cross-border activities Israel has speeded up construction of a wall fitted with an electronic alert system along its 240-kilometre (150-mile) border with Egypt.