Egypt's Muslim Brotherhood has accused the Israeli spy agency Mossad of being behind Sunday's attack on an Egyptian checkpoint on the border with Israel.
Israel's foreign ministry has dismissed the allegation as "nonsense".
The attack left 16 Egyptian security officers dead. Israeli forces say they later killed at least seven gunmen who broke through into Israel.
Israeli and Egyptian officials have blamed the attack on Islamist militants.
A statement on the Muslim Brotherhood's website said the incident "can be attributed to the Mossad".
It said Israel had carried out the attack in an attempt to undermine the government of Egypt's Islamist President, Mohammed Mursi.
The allegation was echoed by Hamas, the Palestinian offshoot of the Muslim Brotherhood that governs Gaza.
"Israel is responsible, one way or another, for this attack to embarrass Egypt's leadership and create new problems at the border in order to ruin efforts to end the [Israeli] siege of the Gaza Strip," the group's prime minister in Gaza, Ismail Haniya, was quoted saying by the Reuters news agency.
Israel's foreign ministry spokesman, Yigal Palmor, denied the accusation, saying: "Even the person who says this when he looks at himself in the mirror does not believe the nonsense he is uttering".
Earlier on Monday, Egypt's state news agency quoted a top security official as saying that the attackers were "jihadists" who had infiltrated from the Gaza Strip.
A statement by the Egyptian military described them as "enemies of the nation who must be dealt with by force". The country has declared three days of national mourning for the dead officers.
Patrols have been stepped up in the Northern Sinai, and Egypt's Rafah border crossing to Gaza has been indefinitely closed as security forces hunt the remaining attackers.
The raid comes amid growing fears that jihadists have gained a foothold in the thinly populated area.
It happened at about 20:00 local time (18:00 GMT) on Sunday, when the sun was setting and the guards had stopped work for the traditional iftar meal, which breaks the daily fast during the Islamic holy month of Ramadan.
About 35 masked gunmen dressed as Bedouin nomads opened fire on the border post, near the Rafah crossing, with guns and rocket-propelled grenades, killing 16 soldiers and border guards and wounding another seven, the Egyptian army said.
The gunmen then approached the Israeli border near the Kerem Shalom crossing with two vehicles, one of which exploded on the frontier, Israeli officials said.
But the second - an armoured personnel carrier - broke through and travelled about 2km into Israel before being disabled by the Israeli air force, according to the officials.
At least five people died inside the vehicle, while two were killed in a gunfight outside, according to Israeli media reports.
'Cowardly'
The aim was to target Israeli civilians, according to Israeli officials. Defence Minister Barak said a major attack had been averted, and called the incident a wake-up call for Egypt.
At an emergency meeting with military and security officials early on Monday, President Mursi condemned the "cowardly" attack and said the security forces would "take full control" of the Sinai peninsula.
Israeli officials believe a brand of radical Islamism is spreading among the tribesmen of the northern Sinai.
Islamist militants have been blamed for several rocket attacks against Israel and a cross-border raid that killed eight Israelis last year.
The rising violence in the area is a test of credibility for the government of President Mursi, the BBC's Kevin Connolly says.
Israel wants tighter security in the Sinai, but it does not want that to be achieved with a large increase in numbers of Egyptian troops near its border, our correspondent adds.
Egypt's military sent extra tanks and troops into the Sinai last year, under terms that had to be agreed with Israel under the 1979 peace treaty between the two countries.
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