Tony Blair said the world must be "firm, united and resolute" in the wake of bombings in the Egyptian resort of Dahab, which killed at least 23 people.
Three explosions occurred in a bustling tourist area
Two Britons were among the injured and are being treated at a Cairo hospital.
One of them Henry Luce - the cousin of the Lord Chamberlain, head of the Queen's household - is in a "stable" condition, his family said.
A doctor named the other injured British national as Sam Still. Worried UK relatives can call 020 7008 0000.
Foreign Secretary Jack Straw has also condemned the "callous terrorists" behind the attacks.
Three explosions occurred in a bustling area popular with tourists during the early evening when many people would have been out in cafes and restaurants.
Unity and 'determination'
The prime minister offered his "sympathy and condolences" to the families of those killed and people who were injured.
He also stressed that the Egyptian authorities had Britain's "total support and solidarity".
Mr Blair went on: "What is important is that the whole world stands united against the terrorists that want to kill innocent people and prevent countries like Egypt making the progress they and their peoples want to see."
He condemned those who attempt to "stop governments functioning properly" and do so "through the slaughter of innocent people".
"We have got to be firm, united, resolved in our determination to stop it," said Mr Blair.
Meanwhile, the foreign secretary said he had sent a message of condolence and solidarity to Egyptian Foreign Minister Ahmed Aboul-Gheit, and was in close contact with the Egyptian authorities.
"Once again terrorists have demonstrated their callous disregard for human life," said Mr Straw.
The three blasts occurred at around 1900 (1800 BST) in a busy shopping and restaurant area close to the seafront, eyewitnesses said.
Dahab is a low-key resort popular with Western backpackers, divers and budget Israeli tourists.
Meanwhile, Buckingham Palace has confirmed that Mr Luce is a cousin of Lord Luce, the Lord Chamberlain, head of the Queen's household.
"Lord Luce has been in touch with his family and the emergency services. It is a private matter," said a palace spokesman.
Two British Red Cross delegates are travelling to Egypt to offer help and emotional support to Britons who have been affected by the blasts.
And the British ambassador, Sir Derek Plumley, told BBC News he and a team from the British consulate in Cairo had opened temporary offices in Dahab and Sharm el-Sheikh "just to check with regard to other British citizens who are here at the present moment who might have concerns".
The two injured British nationals were not thought to be in a "critical condition", he added.
Dahab was a "very, very beautiful place" and it was "particularly sad" the bombings had happened there, Sir Derek told BBC News, adding that tourism was "vitally important" for Egypt.
The blasts occurred in a busy shopping and restaurant area
Middle East analyst Simon Henderson told BBC News the Egyptian government would be "tremendously embarrassed".
"They try to make out Egypt is a friendly and attractive place for foreigners," he added.
The main suspects would be a local group "inspired" by al-Qaeda, Mr Henderson.
Southern Sinai peninsula resorts have been hit several times by bomb attacks.
Sixty-four people, including 11 Britons, were killed last July in a similar attack in Sharm el-Sheikh, further south along the coast.
BBC security correspondent Gordon Corera said the latest bombs - "bags of explosives left in various shops and cafes" - had been "slightly more primitive" than those used in the previous attacks.
"Those previous attacks were blamed on local militants supported by Bedouin tribes from the Sinai aggrieved at both the Egyptian state and foreign tourists coming in.
"And there had been talk that a number of people involved with those previous attacks were still at large."
The "initial working assumption" was a local group "inspired by but not directed by al-Qaeda" was responsible, Corera added.
Steve Riches, from Essex, said he had been about 100 metres from the first two explosions.
He told BBC Radio Five Live he and his friends, who are trained diving instructors, tried to help with first aid.
"As we realised what was going on and tried to make our way out of the restaurant, the third bomb blast went off and that was about 60 or 70 metres away, so pretty loud, pretty scary," he said.
"We got involved as much as we could while trying to keep to a relatively safe distance.
"It was pretty chaotic and pretty confusing."
Another British tourist, Paul McBeath, said the blasts came with "no warning whatsoever".
He told Sky News: "There were just three loud bangs and people rushing around. Everybody is shaken."