Mr Bush has sent Secretary of State Condoleezza Rice back to the Middle East to win support in Beirut and Jerusalem for quickly deploying a UN-backed force.
The president held talks with Mr Blair on the Middle East crisis at the White House on Friday.
But the two leaders refused to call for an immediate ceasefire between Israel and the Lebanese Hezbollah militia, locked in bloody conflict for nearly three weeks, saying a more comprehensive solution was needed.
"This is a moment of intense conflict in the Middle East. Yet our aim is to turn it into a moment of opportunity and a chance for a broader change in the region," Mr Bush said.
The two leaders had harsh criticism of Iran and Syria, Hezbollah's backers, with Mr Blair warning that they must become "proper and responsible members of the international community" or face "the risk of increasing confrontation."
Three-step plan
Mr Bush and Mr Blair outlined a three-step plan to ending the crisis, isolating
Hezbollah as well as its patrons Iran and Syria, and setting the stage for a long-term solution for the Middle East.
Secretary Rice is due to arrive in the region on Saturday "to work with Israel and Lebanon to come up with an acceptable UN Security Council resolution" to end the conflict and set the stage for sending the international deployment, Mr Bush said.
On Monday world powers will meet at the United Nations to decide the size, composition and mandate of the multinational force, paving the way for the Security Council to take up a resolution on the conflict, Mr Blair said.
"Our goal is a Chapter 7 resolution setting out a clear framework for cessation of hostilities on an urgent basis, and mandating the multinational force," Mr Bush said.
That section of the UN charter invokes the need "to maintain or restore international peace and security" and provides for the possible use of sanctions or military force.
"This can only work if Hezbollah are prepared to allow it to work," Mr Blair said.
"If they stand out against that, then it's not merely that they will be doing a huge disservice to the people of Lebanon, but they will also, again, face the fact that action will have to be taken against them," he said, without saying who would take such action.
Mr Bush, who announced US plans to help rebuild Lebanese homes and infrastructure, said a chief goal of an international force was to allow the Lebanese armed forces to secure southern Lebanon and disarm militia groups.
"An effective multinational force will help speed delivery of humanitarian relief, facilitate the return of displaced persons, and support the Lebanese government as it asserts full sovereignty over its territory and guards its borders," President Bush said.
Under fire for giving Israel a free hand to strike at targets in Lebanon, Mr Bush and Mr Blair insisted on the urgent need for an end to the conflict and said Ms Rice's mission was a testament to their commitment to do so.
"We agree that a multinational force must be dispatched to Lebanon quickly to augment the Lebanese army as it moves to the south of that country," Mr Bush said.
A senior State Department official with Secretary Rice in Kuala Lumpur, where she has been attending Southeast Asia's top security forum, said she would return to Jerusalem on Saturday.
"She will go where she needs to go to get progress," the US official said, adding that "this thing is evolving hour by hour."
Ms Rice flew to Malaysia for the ASEAN Regional Forum, a gathering of Southeast Asian nations and key security partners, including the US, Russia and China, after a tour of Beirut, Jerusalem, the West Bank and a crisis meeting in Rome on Wednesday.
The Rome conference brought together 15 nations but failed to produce a call for an immediate ceasefire, adding support to the US and British position that there must first be a sustainable solution to the conflict.
More than 420 people, mostly civilians, have died in Lebanon since Israel launched its massive offensive after Shiite militants of Hezbollah captured two soldiers and killed three more in a cross-border raid on July 12.
A total of 51 Israelis have also died, the majority of them soldiers.