"The alliance must maintain its resolve and finish the fight ... we cannot afford to loose Afghanistan," he said.
"To ensure that we do win, France is sending additional forces to Afghanistan, the United States is deploying an additional 3,500 marines. Romania is adding forces, as are several other allies.
"We ask other Nato nations to step forward with additional forces."
Bush also spoke of his commitment to building a missile-defence system in Europe and will urge Vladimir Putin, Russia's president, to drop his objection.
Putin will attend the summit - set to run until Friday - when he will meet Nato leaders.
Bush said that Nato had outlived the so-called Soviet threat that it was created to destroy and must now act as "an expeditionary alliance" around the world.
"Our alliance must maintain its resolve and finish the fight in Afghanistan," he said.
Ukraine and Georgia
Bush also renewed calls for Nato to start the admission process for Ukraine and Georgia despite a split among alliance members and fierce Russian objections.
Bush said the two former Soviet republics are ready for membership and that Nato leaders at a summit this week must make clear that membership will remain open to all European nations, no matter what Moscow thinks.
"We must make clear that Nato welcomes the aspirations of Georgia and Ukraine for membership in Nato and offers them a clear path forward toward that goal," he said.
|Bush arrived in Romania on Wednesday to|
attend a summit of Nato leaders [AFP]
"So my country's position is clear: Nato should welcome Georgia and Ukraine into the Membership Action Plan. And Nato membership must remain open to all of Europe's democracies that seek it, and are ready to share in the responsibilities of Nato membership."
Jonah Hull, Al Jazeera's correspondent in Kiev, said: "Ukraine and Georgia are unlikely to be given this membership action plan in Bucharest.
"The problem they face even with president Bush's support is opposition both from Russia and from significant members of the Nato alliance.
"Russia has long been wary of Nato's expansion eastwards. It views it as a provocation and even says it will aim missiles at Ukraine if it goes ahead."
Earlier, Bush was in Ukraine on Tuesdsay where he backed the country's attempt to join Nato after meeting Viktor Yushchenko, his Ukrainian counterpart.
He said Ukraine's support for the missions in Afghanistan and Kosovo had boosted its effort to join the organisation.
"Ukraine now seeks to deepen its co-operation with the Nato alliance through a membership action plan," Bush said at a news conference with Yushchenko.
Bush urged Russia on Tuesday to join the planned US missile shield he said was "urgently needed" to thwart a possible threat from Iran.
Bush said that a US plan to set up bases in Europe for an intercontinental missile defence shield was not an "anti-Russian" move.
"We're dealing with a lot of history and a lot of suspicion ... I'm hopeful we'll have some breakthroughs, we'll see," he said.
"Obviously we've got work to do to persuade the president and the people around him that the missile defence system is not aimed at Russia."
The US has said it plans to station missiles in Poland and a radar system in the Czech Republic to counter potential threats from "rogue" states such as Iran or North Korea.