Blair held talks with Iraqi Prime Minister Nouri al-Maliki in a visit designed to show support for fragile attempts to halt continuing bloodshed in the country.
Blair, who is traveling the Middle East to push for Israeli-Palestinian peace, was whisked into the heavily fortified Green Zone from the airport on a military helicopter. He had flown to Baghdad by a Royal Air Force transport plane from Cairo. It was his sixth visit to the country since the U.S.-led 2003 invasion.
During a joint news conference with al-Maliki, the British prime minister stressed the importance of "all countries in the region" supporting the fledgling Iraqi government, and insisted Iraq had made progress since the toppling of Saddam Hussein.
"Our task — ours, the Americans, the whole of the coalition, the international community and the Iraqis themselves — is to make sure that the forces of terrorism don't defeat the will of the people to have a democracy," Blair said at a news conference with al-Maliki.
Blair rejected a suggestion that the sectarian bloodshed being experienced across the country was created by the U.S. and British decision to invade, saying the challenge in Iraq was part of a wide struggle against those opposed to democracy.
"There is innocent blood being spilt, but it's not being spilt by the Iraqi government democratically elected or by those supporting them. It's being spilt by the very forces that worldwide are trying to prevent moderation, prevent modernization, prevent people expressing their will through democracy rather than through violence," he said.
Late on Sunday afternoon, Blair flew to Basra to visit some of the troops stationed there.
In a cavernous hangar and before a backdrop of a Lynx helicopter, Blair told some of the 7,000 British troops serving in southern Iraq that they were fighting on behalf of "people of tolerance and moderation" around the world.
"This is real conflict, real battle, and it is a different kind of enemy not fighting a state, but fighting a set of ideas and ideologies, a group of extremists who share the same perspectives," Blair said. "What we need to try to do is build an alliance of moderate people against the extreme."
During what has become an annual holiday-season visit to the region, Blair told troops that extremism was causing havoc in neighborhoods from Basra to London a reference to the July 2005 transit bombings in the British capital.
"The crazy thing about today's world is it actually comes back to our own streets," he said. "All over the world the same struggle is going on, and if we don't stand up and fight for the people of tolerance and moderation who want to live together, whatever their fate, then the people of hatred and sectarianism will triumph."
Battling extremism has been the theme of Blair's trip to the region, which began in Turkey, moved to Egypt, and is to continue in Israel, the Palestinian Territories, and the United Arab Emirates.
"Our country and other countries like it are having to rediscover what it means to fight for what you believe in," Blair told the soldiers.
Britain has the largest commitment of troops in Iraq of any country after the United States. More than 120 British personnel have died in the country since the U.S.-led invasion in 2003 that ousted Saddam Hussein.
British officials said several thousand troops are expected to be withdrawn from Iraq next year.
Blair gave no new details, however, of when troops might leave Iraq.
Meanwhile, in other developments:
The soldiers were conducting a patrol to clear a route so that another unit could move through the area on Saturday, the military said in a statement. A bomb exploded near one of their vehicles, the statement said.
The toll raised to 57 the number of Americans killed in Iraq in December. At least 2,945 members of the U.S. military have died since the U.S.-led invasion in March 2003, according to an Associated Press count.
A Red Crescent official said the gunmen left women behind at the office in Andalus square. The official spoke on condition of anonymity because of safety concerns.
The Red Crescent, which is part of the international Red Cross movement, has around 1,000 staff and some 200,000 volunteers in Iraq. It works closely with the International Committee of the Red Cross, which visits detainees and tries to provide food, water and medicine to Iraqis.
Mazin Abdellaha, the secretary-general of the Iraq Red Crescent, appealed to the kidnappers to release the captives.
"They represent a humanitarian agency that works for the general good, and this agency helps all people regardless of their sect or ethnicity," Abdellaha said.
At least half a dozen mass kidnappings have been carried out in the Iraqi capital this year, possibly by armed groups linked to the sectarian conflict between Sunnis and Shiites.
But key players on both ends of the Sunni-Shiite divide skipped Saturday's meeting, raising doubt that the conference will succeed in healing the country's wounds.