Britain's Foreign Secretary Margaret Beckett said it showed the U.S. and Iraqi governments are determined to deal with the security situation.
And in Australia, Prime Minister John Howard said Bush has chosen the proper course.
"The alternatives the president faced were either to announce what he announced or effectively indicate that the West could not win in Iraq and start making arrangements -- however it might be camouflaged -- for a withdrawal," Howard said. "I believe, in the circumstances, the president chose the only realistic option."
More Troops, More Money
But Britain and Australia say they do not intend to contribute any extra troops themselves.
The main points of Bush's plan are to send 21,500 more troops to Iraq, mostly to Baghdad, with the first soldiers set to arrive this month.
There will be economic aid too, and -- if Congress approves -- $5.6 billion to cover the cost of troop increases.
Bush also outlined steps he expects the Iraqi government to take -- including adopting a law to share oil revenues among all Iraqis, a move designed to draw minority Sunnis into the political process.
And he said Iraqi forces would take over responsibility for security by November.
That's something Iraqi government spokesman Ali al-Dabbagh welcomed today.
"The political part of the U.S. strategy is an Iraqi vision. The good thing about this plan is that it acknowledges that responsibility for security should be handed over to the Iraqis," al-Dabbagh said. "Trained and equipped, the Iraqi forces will be more capable of protecting Iraq's security."
Iraqi Foreign Ministry Undersecretary Muhammad al-Haj Mahmud told RFE/RL's Radio Free Iraq that his government endorses new efforts to boost its authority.
"According to my own understanding of the new strategy, it has two main objectives," Mahmud said. "The first is to help maintain security. The second and fundamental objective is to build up capabilities of the Iraqi security forces, both army and police, to be able to assume responsibility for Iraq's security as of November. This second objective is what the Iraqis are counting on."
"Without an effective Iraqi government capable of running the country in a sound way without administrative corruption and without dragging its feet, a new Iraq cannot be built no matter how strong a strategy may be," he added. "When President Bush points that out, he is absolutely right."
Not surprisingly, some leaders of Iraq's Sunni minority were less supportive.
"We don't think the new, additional forces will present a satisfactory solution to Iraqis, either politicians or resistance," lawmaker Nuraldin al-Hayali, of the Sunni-led Iraqi Accordance Front told RFE/RL. "They will be a very transient solution, but deploying these forces has implications that go beyond security."
Others have been more cautious -- or critical.
France, which opposed the 2003 U.S.-led military intervention in Iraq, said today that Bush's proposals do not go far enough.
"The situation in Iraq is seriously worsening day by day," French Foreign Minister Philippe Douste-Blazy said in Paris today. "Beyond the proposals that have just been made by President Bush, we think that the only solution that will allow Iraq to recover its stability, its sovereignty, its territorial integrity, and its national unity, lies in the participation of all parts of Iraqi society -- civil, political and religious."
Siamak Herawi, a deputy spokesman for Afghan President Hamid Karzai, offered only cautious support for Bush's initiative.
"Afghanistan, which has a lot of experience with war and destruction, wants that the killings between brothers and the destruction to end immediately," Heraqi told RFE/RL's Radio Free Afghanistan. "If the changes in the strategy of the United States result in peace in that country, Afghanistan supports that strategy."
Syria's government daily "Tishrin" said the plan is likely to fail due to the complexity of the situation in Iraq.
Iranian Foreign Ministry spokesman Mohammad-Ali Hosseini condemned it as "just another effort to continue the occupation."
European Commission spokeswoman Emma Udwin today said the bloc hopes the new measures lead to greater stability in Iraq, and welcomed what she called Bush's "more comprehensive approach."
"The answers to this situation are to be found not only in security measures but, more broadly, in a range of measures, including the political and a national reconciliation process, and all of these need to be addressed in parallel," Udwin said.
The Sectarian Question
Some experts, too, are wondering whether the steps Bush outlined will really help curb the sectarian violence -- or whether putting in extra troops might even have the opposite effect.
One such expert is defense analyst Timothy Garden of King's College London. He recalls the major U.S. assault on the insurgent stronghold of Al-Fallujah in 2004, which involved intense fighting and caused widespread destruction.
"Sustaining a presence on the ground and at the same time not risking large prolonged casualties to American forces over a period of time doesn't seem possible," Garden said. "So I think it is unlikely that this will make much of a positive difference. One of the other elements of what's being suggested is that the rules of engagement would become even more robust -- I think that was the phrase used in one of the briefings -- which sort of suggests that this might come to be a Fallujah-style approach in Baghdad. And that almost certainly will stir up more violence and make the situation worse."
Another question is whether the extra 17,500 troops targeted for Baghdad can really make a difference in a city of 6 million, and whether the troop increases will last long enough.
The United States has tried before to secure Baghdad by putting extra troops on the streets, most recently last summer.
Since that failed, what -- some are asking -- makes this time any different?
In his speech, Bush said two things are different now. First, there weren't enough Iraqi and U.S. troops then to secure neighborhoods after they were cleared of insurgents. Second, he said, there were too many restrictions placed on the troops that were there.
Joost Hiltermann, a political analyst with the International Crisis Group in Jordan, says a military approach will not work unless the country's political actors come together.
"A military initiative will simply fight symptoms but not the underlying problems," Hiltermann said. "The main problems are the differences over the nature of the federal system for Iraq; the issue of oil revenue sharing; the issue of de-Ba'athification, and then there are a number of lesser issues. Those are the key issues."
Some experts have another question -- whether Bush's plan is asking too much of Iraq's Shi'a-dominated government. Is the Iraqi government committed, they ask, to building a society that is truly inclusive of all of Iraq's various religious and ethnic communities?
And if it is committed, how will it achieve this without alienating key constituencies, which include Shi'ite religious groups and militias?
The answers to these questions will be crucial in determining the ultimate result of Bush's new approach.
The Imam Al-Mahdi Army on parade (epa)
HAS THE CONFLICT IN IRAQ BECOME A CIVIL WAR? Many observers have concluded that the tit-for-tat sectarian violence that emerged after the February 2006 bombing of a mosque in Samarra has become a full-blown civil war.... (more)
U.S. Media Starts Using 'Civil War' Label
Iraqi Prime Minister Under Fire From All Sides
U.S. Expert Discusses Prospects For Stabilization
President Says Iraq Needs Iran's Help
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THE COMPLETE PICTURE: Click on the image to view RFE/RL's complete coverage of events in Iraq and that country's ongoing transition.