(CNN) -- As Egyptian authorities vowed quick vengeance for a terrorist attack that killed 16 soldiers, officials in Egypt and Israel disagreed as to who was to blame for the bloodshed.
On Sunday, attackers with semiautomatic weapons and hand grenades stole two armored vehicles from Egyptian forces and tried to enter Israel.
Israel blamed militants associated with the group Global Jihad for the violence. Egyptian military officials called the attackers "enemies" of the nation. The Muslim Brotherhood accused the Israeli intelligence agency Mossad for the killings.
Egyptian President Mohamed Morsy, who resigned from the Muslim Brotherhood before he took office recently, condemned the attack, which also wounded seven soldiers, three critically. He vowed Monday "to capture those who conducted this traitorous attack on our sons."
Morsy and Egypt's long-time top military leader, Field Marshal Muhammad Tantawi, visited Monday the area where the attack on the troops, who were breaking their Ramadan fast at sunset, took place.
According to the Supreme Council of the Armed Forces, there were 35 assailants -- terrorist factions from Gaza, it said -- involved in the attack near the Rafah border crossing in the Sinai, a restive area of Egypt where there have been kidnappings and armed clashes in recent months.
"Egyptians will not have to wait long before they see a reaction to this attack by terrorists," the SCAF said on its Facebook page.
Eight attackers were killed by Israeli forces, Israeli Defense Minister Ehud Barak told a TV audience.
One of the vehicles exploded at the border, and the other was attacked by Israel's air force as it was entering Israeli territory, a spokesman for the Israel Defense Forces said.
The Rafah border crossing has been closed indefinitely, North Sinai security official Ahmed Bakr said. And more Egyptian military forces have been deployed to the area to assist.
"Our forces will impose a full control on these areas," Morsy said in an address to the nation. "Sinai is safe and fully under control -- those who did this will pay a high price."
The Israeli Foreign Ministry issued a statement Monday giving "condolences to Egypt and to the Egyptian people" after the attack, which "was meant to slay Israelis as well." The violence was "aimed at shattering the peace agreement between Israel and Egypt," it said.
Barak briefed a Knesset subcommittee on the incident.
"IDF forces ... showed vigilance, sharpness, and purposefulness in thwarting the terrorist attack that could have caused many casualties," he said. "The terrorists' operational means once again demonstrate the need for a determined move by our Egyptian counterparts in order to enforce the rule of law and security in the Sinai region."
According to the Israel Defense Forces website, IDF spokesman Brig. Gen. Yoav Mordechai said Sunday that Israel had obtained intelligence before the attack that "enabled the IDF to prevent the Global Jihad terrorists from infiltrating from Egypt into Israel. This is an extremely serious incident."
The IDF is "is in contact with the Egyptians and we will study this event, which is a product of the terror infrastructure in Sinai."
"We tracked this attempted attack, and fortunately there are no injuries among IDF forces or residents of the area," Mordechai said.
In recent months, Israeli forces have been involved in clashes with militants near the Jewish state's border with the Sinai. In June, attackers fired on Israelis working on the security barrier between the two countries.
Egyptian intelligence officials have said that cells of al Qaeda and other extremist groups are operating in Sinai.
Americans have been abducted in Sinai and then released shortly afterward several times so far this year.
Kidnappings and armed robberies have increased since a popular uprising ousted Egypt's long-ruling dictator, Hosni Mubarak, last year.
Morsy called on the military council Monday to hold an emergency meeting, state TV in Egypt reported.
Hamas, the movement that controls the Palestinian territory of Gaza, condemned the Sunday attack, calling it an "ugly crime."
Hamas officials closed all border tunnels connecting Gaza with Egypt after of the attack, according to Tahir Al-Nono, a spokesman for the Palestinian Authority in Gaza.
CNN's Salma Abdelaziz, Yousuf Basil and Talal Abu-Rahma contributed to this report.