But this will be a challenge for Mr. Bush, who arrived Monday night in Kiev, Ukraine, at the start of a trip that also will include Romania, Croatia and Russia. The NATO alliance is strained currently and is engaged in soul-searching about its place and mission in a rapidly changing world.
Beyond Afghanistan, Mr. Bush is trying to score a breakthrough on a U.S.-based missile defense system in Europe. And he wants NATO to expand its borders.
Speaking at a news conference Tuesday with Ukraine's president in the country's capital of Kiev, Mr. Bush said he would work as hard as he can to help Ukraine join the NATO alliance, and he declared that Russia will not have a veto over the matter.
Mr. Bush praised democratic and military reforms undertaken to help support Ukraine's bid for NATO membership. He said that the United States "strongly supports" Ukraine's request to get an outline for what it needs to do to join out of this week's NATO summit.
The President spoke after talks with his counterpart, President Viktor Yushchenko. The Ukrainian leader said he is sure his country will "receive a positive signal" during the summit. At the summit, NATO leaders are expected to formally invite Croatia, Albania and perhaps Macedonia to join, expanding the alliance's imprint in the Balkans. Mr. Bush supports that expansion and also wants Ukraine and Georgia to get on track for membership.
At the center of the trip is the NATO summit, starting Wednesday in Bucharest, Romania. The war in Afghanistan is under fresh review as the 26-nation NATO alliance confronts al Qaeda and Taliban forces, rising violence and internal debate about whether member nations are contributing enough.
Mr. Bush's administration expects to emerge from the summit with a strong allied statement about the commitment in Afghanistan - a message that could be backed by the limited promise of new troop deployments to Afghanistan, where NATO commanders say they need more muscle.
"We think we're going to have some countries stepping up and doing more in Afghanistan," Stephen Hadley, the president's national security adviser, told reporters traveling with Mr. Bush on Air Force One. He declined to name those countries or say whether their expected troop additions will be enough.
"Let's see what we get," Hadley said. "We've all been saying that we all need to do more. We've also been saying this is going to be a long effort."
"I would be surprised if we saw commitments in Bucharest at a level that would fully meet all the requirements" for combat troops and military and police trainers, Gates said. "But we'll just keep working at it."
The United States wants not only more troops, but also fewer restrictions from some governments on how their troops can be used. Those restrictions are intended to limit the risk of casualties; U.S. officials complain that they also limit the usefulness of the forces.
Mr. Bush's push for more NATO support comes days after a new warning from CIA Director Michael Hayden that al Qaeda militants regrouping in the Pakistan border region pose an increasing threat to Afghanistan, and the West. Taliban subcommanders claim 4,000 militants are about to be moved from training camps in Pakistan across the border into Afghanistan, and dozens more are being trained separately to wage attacks in the West.
NATO's force is about 43,000-strong, but commanders are pleading for more troops in the south, where Taliban insurgents are wreaking the most havoc.
The United States is the biggest contributor of troops in Afghanistan, with 31,000 fighting men and women - about 17,000 as part of the NATO-led force, and 14,000 in a U.S.-led outfit in eastern Afghanistan that is training the Afghan army and conducting counterinsurgency operations.
Most of the fighting is done by troops from the U.S., Canada, Britain and the Netherlands.
Ahead of Mr. Bush's trip, French President Nicolas Sarkozy, for one, pledged to deploy more troops to fight the Taliban if Afghans also get more responsibility and if there is better coordination of nonmilitary efforts. Mr. Bush said that promise would help ensure the NATO meeting is a success.
Some European leaders are under pressure to pull back, though, and NATO is increasingly stretched thin.
Mr. Bush starts in Ukraine in a show of support for the country's democratic reforms. He meets Tuesday with the country's leaders and its opposition leader. The president and first lady Laura Bush are also set to visit a cathedral and a public school before departing for Romania.
Meanwhile, Mr. Bush also has an upcoming date with Russian President Vladimir Putin.
At week's end in the Black Sea resort city of Sochi in Russia, the two will again discuss the missile defense system that the United States plans to base in Central Europe. It would involve 10 interceptor missiles based in Poland and a tracking radar system in the Czech Republic.
Moscow has been vehemently opposed to the idea, saying the intent is to weaken its nuclear deterrent. The United States denies that.
Speaking in Kiev on Tuesday, Mr. Bush said it was "in Russia's interest" to work with the United States to develop the anti-missile system.
Hadley said Mr. Bush had talked to Putin about the matter personally, and in a letter he sent to Putin. He sounded optimistic about a breakthrough. The meeting in Sochi will be the last encounter between the two men before Putin steps away from the Russian presidency.
"We're hopeful," Hadley said. "We're not going to resolve all our differences. You know, this is a complicated relationship."
Before leaving Washington, Mr. Bush could not help but poke Congress on his way to his helicopter.
He said lawmakers in the Democratic-run Congress should pass a Colombia free-trade deal, a reform of the Federal Housing Administration and a government eavesdropping law intended to root out suspected terrorists. "They have a lot of work to do," Mr. Bush said.