More than 900 people were killed in the fighting and several parts of Lebanon were reduced to rubble by Israeli forces responding to the murder of three Israeli soldiers and the kidnapping of two others when Hezbollah terrorists crossed the border into Israel on July 12. Bush said the "responsibility for this suffering lies with Hezbollah."
"Responsibility for the suffering of the Lebanese people also lies with Hezbollah's state sponsors: Iran and Syria. The regime in Iran provides Hezbollah with financial support, weapons and training," Bush said during a visit to the State Department.
"The [U.N.] resolution calls for a robust international force to deploy to the southern part of the country to help Lebanon's legitimate armed forces restore the sovereignty of its democratic government all Lebanese territory," the president said.
Bush's remarks followed those by a State Department spokesman who said if the U.N.-declared cease-fire is fully implemented, it will be a strategic setback for Iran and Syria because it will strengthen Lebanese democracy and stabilize the border with Israel.
"You will not have Hezbollah roaming freely in the south of Lebanon," spokesman Sean McCormack said. "Iran and Syria will not have had the ability to rearm Hezbollah."
Hezbollah's leader Sheik Hassan Nasrallah also claimed victory in the 34-day conflict between his fighters and Israel.
But Bush said the victory belongs to Israel and the rest of the world, which will see Hezbollah disarmed. He added that Hezbollah runs a very big propaganda machine. The U.S. has designated Hezbollah a terrorist organization.
"If I were Hezbollah, I'd be claiming victory too. ... But how can you claim victory when, at one time, you were a state within a state, safe within southern Lebanon, and now you're going to be replaced by a Lebanese army and an international force?"
The U.N. resolution sets the stage for 15,000 Lebanese troops and 15,000 foreign troops to be deployed in southern Lebanon, the main staging area for decades of Hezbollah cross-border attacks on Israel.
Two years ago, the U.N. Security Council required Hezbollah to disarm, and that principle is carried over by the new resolution approved unanimously last week. McCormack said when the two resolutions are implemented, "that would represent a setback for Hezbollah."
Estimates vary as to how long it might take to assemble an international force and deploy it in Lebanon. "We are pushing for this force to be generated as quickly as possible," McCormack said. The United Nations has had two preliminary planning sessions and a larger one is expected later in the week.
"I would hope that very quickly we would see countries coming forward and saying that they will participate in the force," the spokesman said.
McCormack said France was likely to play a leading role.
As for the international force, he said, "What we have is the version of UNIFIL [United Nations Interim Force in Lebanon] with an 'S' on its chest as opposed to the Clark Kent version of UNIFIL."
Bush said implementing the U.N. resolution will be crucial in the effort to get people to realize the stakes involved and the value of innocent life that was lost so unnecessarily. But implementing the multinational force is not the only measure spelled out in the Security Council's resolution.
"Part of the mandate in the U.N. resolution was to secure Syria's borders. Iran is able to ship weapons to Hezbollah through Syria. Secondly is to help seal off the ports around Lebanon.
"As well, there's the diplomatic mission that needs to be accomplished. In other words, the world must now recognize that it's Iranian sponsorship of Hezbollah that exacerbated the situation in the Middle East," Bush said. "Iran has made clear that it seeks the destruction of Israel. We can only imagine how much more dangerous this conflict would be if Iran attained the nuclear weapons it seeks."
The president said that Syria permits Hezbollah leaders to operate out of Damascus and gives political support to Hezbollah because it wants to undermined Lebanon's government and regain dominance in that country.
The U.N. resolution calls for Israel not to take any offensive action before the peace force arrives. Asked what he would describe as appropriate action, Bush said Israel can respond freely if defense forces are fired on by the other side.
"As far as I'm concerned, if somebody shoots at an Israeli soldier, tries to kill a soldier from Israel, then Israel has the right to defend herself. She has a right to try to suppress that kind of fire," he said.
In the meantime, Israeli Defense Minister Amir Peretz said Sunday, "There is no situation in which Hezbollah fires at [Israeli] forces that we will not retaliate."
Backing that position, McCormack said, "There is nothing in this resolution that calls upon Israel to abrogate its rights to self-defense."
Private groups that monitor Middle East developments were cautious in their assessments.
Provisions of the resolution are "likely to be realized in part, but none in its entirety," said Geoff Porter, an analyst with the Eurasia group, a consulting firm that advises the U.S. and Japanese governments as well as corporations.
Hezbollah, Lebanese and Israeli positions "will probably conspire to scuttle" the resolution, he said.
Mark Rosenblum, founder of Americans for Peace Now, a dovish Zionist organization, said, "We think that this is a necessary and potentially important piece of paper."
"But the hard work in establishing peace on the ground has just begun, particularly for the Bush administration," Rosenblum said.
The Associated Press contributed to this report.Complete coverage of the Mideast Meltdown is available in FOXNews.com's Mideast Center.