Hosni Mubarak, the Egyptian president, vowed that the perpetrators would be punished. Egypt has been a target of Islamist attacks targeting foreigners since the early 1990s.
"The perpetrators of these heinous acts of terrorism will be tracked down and punished," Mubarak said.
Ehud Olmert, Israel's prime minister-designate, telephoned Mubarak to express his condolences and his office said "the two leaders discussed the need for co-operation between the two countries in the fight against international terrorism".
Egypt declined an offer from Shaul Mofaz, the Israeli defence minister, to send army rescue teams and doctors, as hundreds of Israeli tourists rushed home after the attacks.
A state of alert was declared at the main hospital in the Israeli border town of Eilat to handle any casualties sent for treatment there. Three Israelis were injured, according to army radio.
About 5,000 Israeli holidaymakers were believed to have been in the Sinai at the time of the blasts despite repeated warnings from their government of the risks of attack by Muslim fighters.
George Bush, the US president, called it a "heinous act against innocent civilians".
Bush, seeming to equate the perpetrators of the attacks in Dahab, on the Sinai peninsula, with al-Qaeda fighters who carried out the September 11, 2001, attacks in the US, said: "Today, we saw again that the terrorists are willing to try to define the world the way they want to see it."
A restaurant's wrecked fish stall
after the triple bomb attack
He said: "I strongly condemn the killings that took place, the innocent lives lost.
"I assure the enemy ... we will bring them to justice for the sake of justice and humanity," he said.
No one immediately claimed credit for Monday's attacks, which came one day after a new audiotape of al-Qaeda leader Osama bin Laden surfaced accusing the "Crusaders" of the West of waging war against Islam.
Jack Straw, the British foreign secretary, described the bombings as "appalling", targeting as they did a popular holiday resort on an Egyptian public holiday.
"Once again terrorists have demonstrated their callous disregard for human life," he said.
Jacques Chirac, the French president, expressed his "consternation" and "categorically condemned these odious terrorist acts," according to a statement from his office, which said Paris "stood side by side with Egypt in the fight against terror".
Mubarak vowed to track down
and punish the perpetrators
Palestinian leader Mahmoud Abbas branded the attacks as criminal and cowardly, describing the perpetrators as "enemies of humanity", according to a statement from his office.
"This cowardly act which targeted innocent people is the expression of blind hatred of groups which hurt our nation and religion."
His words were echoed by the Hamas-led Palestinian government. "Our government strongly condemns this criminal act which flouts our religion, shakes Palestinian national security and works against Arab interests," government spokesman Razi Hamad told AFP.
In July last year, about 70 people were killed in multiple attacks on Sharm el-Sheikh at the tip of the Sinai and at least 34 lost their lives in bombings in Taba near the border with Israel in October 2004.