Blair, speaking after a meeting between the two leaders, called the blasts that shattered the British consulate and the London-based HSBC bank in downtown Istanbul "the latest terrorist outrage."
Blair said the attacks should not lessen "in any way" the two countries' commitment in Iraq.
"Once again we're reminded of the evil these terrorists pose to innocent people everywhere and to our way life," Blair said. "Once again, we must affirm that in the face of this terrorism there must be no holding back, no compromise, no hesitation in confronting this menace, in attacking it wherever and whenever we can and in defeating it utterly."
Mr. Bush expressed sympathy for the loss of life and said, "The nature of the terrorist enemy is evident once more. We see their utter contempt for innocent life. They hate freedom. They hate free nations."
Blair, who has seen his approval ratings sink amid broad opposition here to the war, called the process of ensuring a stable, democratic Iraq "an essential part in defeating this fanaticism and extremism" that is killing innocents in attacks around the world.
"Our response is not to flinch or give way or concede one inch," he said. "We stand absolutely firm until this job is done."
"They need to be stopped and we will stop them," Mr. Bush said.
Anti-war activists from across Britain traveled to London Thursday for a march aimed at letting the president know of their opposition to U.S.-British policies in Iraq.
Mr. Bush said he was not dismayed by mass demonstrations against his visit.
"Freedom is beautiful," the president said, adding he was happy to be in a country where people were allowed to speak their minds freely. "All I know is that people in Baghdad weren't allowed to do this until recent history."
Police said the heavy security deployed for Wednesday's scattered protests against the president's state visit would again be in place for the march, which organizers hope will attract up to 100,000 people.
Deputy Assistant Commissioner Andy Trotter of London's Metropolitan Police said a small minority of hard-core activists could attempt to cause violence.
"While we expect the march to be peaceful in itself, there will no doubt be elements who try to take advantage to cause problems," he said.
"A number of well-known faces are about and we won't be at all surprised if they tried some sort of concerted action later today," he added.
Earlier, the presidentpaid his respects to Britain's war dead Thursday on his continuing state visit.
At the Tomb of the Unknown Warrior in London, he laid a wreath bearing a red, white and blue banner and bowed his head in prayer.
Mr. Bush will also meet with relatives of the British soldiers and civilians killed in the Iraq war. He says, "we cannot take the pain away, but these families can know that they are not alone."
On Wednesday, Mr. Bush's first full day as guest of Queen Elizabeth II at Buckingham Palace, police often outnumbered protesters who waved placards and chanted their demands that Mr. Bush leave the country.
The crowds reached 500 to 600 outside the palace gates Wednesday afternoon, police said. While the protests were noisy, accompanied by whistles, drums and shouts, they were generally peaceful. There were a few scuffles and police said about 40 people had been arrested since the start of the visit on charges that included theft, drunkenness and drug possession.
Protesters remained outside the palace late into the evening as the president and his wife, Laura, attended a formal dinner there with the queen, members of the royal family and dozens of eminent guests.
Opposition to the invasion of Iraq has been strong and vocal in Britain, and many people are angry that Prime Minister Tony Blair took the country into the U.S.-led coalition against Saddam Hussein.
Thursday's march was to culminate in the planned toppling of a mock statue of Bush in Trafalgar Square. Although it is a weekday, with most people at work, the Stop the War Coalition said that if there was only one anti-Bush event people could support, "this is the one."
Gillian Siddons, a cook from Auchenblae in Scotland, was already protesting Thursday morning. She stood near Westminster Abbey, where Bush laid a wreath at the Tomb of the Unknown Warrior, wearing a sign saying "Who wants democracy Bush-style?"
Siddons, 52, said most British people "don't think his style of democracy is what we want in Britain, and the Iraqis certainly don't want it."
About 100 protesters, watched by a large contingent of police, gathered opposite the entrance to Downing Street, where Mr. Bush and Blair were meeting Thursday. Some wore orange jumpsuits and masks to protest the detention without trial of terrorist suspects at Guantanamo Bay, Cuba.
The protests, which have been brewing for weeks, did not appear to faze the president, who has said repeatedly that he appreciates the freedom of expression that permits such demonstrations. He made light of the opposition on Wednesday, when he jokingly compared his situation to American magician David Blaine's 44-day starvation stunt.
"It was pointed out to me that the last noted American to visit London stayed in a glass box dangling over the Thames," Mr. Bush told an audience of academics at the Banqueting House in central London. "A few might have been happy to provide similar arrangements for me."