And France and Germany renewed calls for a reform of transatlantic relations that would give greater weight to the emerging, enlarged EU as the key US partner, challenging the primacy Washington accords to Nato.
Bush told reporters after a summit of the 26 Nato leaders that the Cold War defence alliance remained the central security organisation binding Europe and the United States.
"I think it is the vital relationship for the United States when it comes to security," he told a news conference. "It is a relationship that ... has worked in the past and is adjusting so that it works in the future."
French President Jacques Chirac said he sensed in talks with Bush on Monday night that the US leader understood what he called the new European reality, in which the EU was taking on ever greater weight, including in defence.
"Europe and the United States are real partners. So we need to dialogue and listen to each other more," he told the summit.
"We must also, as the German chancellor has underlined, continue to take account of the changes that have occurred on the European continent," Chirac said.
Nato Secretary-General Jaap de Hoop Scheffer trumpeted the agreement of all 26 allies to make some contribution to the Iraq training mission as a sign of the alliance's rediscovered unity.
But that boast masked wide divergence in the level of help on offer. France, the most virulent European critic of the war, agreed for just one of its officers at Nato headquarters to help co-ordinate offers of equipment to the Iraqi military.
Asked if he was satisfied with such token contributions, Bush shrugged: "Every contribution helps."
The United States is to provide around 60 trainers out of a total close to 160. France, Germany and Belgium remain adamant that their personnel not serve inside Iraq.
Bush later held talks with the 25-member EU on a tightly scripted day meant to highlight common purpose in rebuilding Iraq and Afghanistan and spreading democracy in the Middle East.
He voiced worries that EU plans to end a ban on arms sales to China could change the balance with Taiwan, which Washington is committed to defend, but hinted he could accept EU assurances that it would not lead to dangerous technology transfers.
Bush said European leaders would have to "sell" such assurances to a sceptical US Congress, which has threatened to curtail military technology sharing with Europe over the issue.
Earlier, Bush met Ukrainian President Viktor Yushchenko, who told Nato leaders his newly democratic country's long-term aim was to join the alliance and the EU.
Bush reaffirmed that Nato's door would stay open to all European democracies but gave no target date for Ukrainian membership, a potential red rag to Russia.
VIRULENT CRITIC: Bush dined on Monday with Chirac, his chief critic in the run-up to the Iraq invasion, in a clear effort to put divisions behind them and seek common ground.
Chirac said he had urged Bush to help France, Britain and Germany in negotiations on Iran's nuclear programme by backing Tehran's bid for World Trade Organisation membership and allowing civil aircraft engine sales.
The US leader has supported the EU diplomatic initiative but given no hint that Washington is willing to offer any such incentive. On Monday, he listed a string of other demands on Tehran including ending support for anti-Israeli militants and allowing greater political freedom.
Chirac and Bush also issued a joint call for a Lebanon "free of foreign domination", ratcheting up pressure on Syria to pull its troops out after last week's murder of former Lebanese Prime Minister Rafik al-Hariri, which critics blamed on Damascus.
POLICE FIRE TEARGAS: Belgian police fired teargas at hundreds of demonstrators protesting against the visit of US President George W. Bush to European Union headquarters on Tuesday.
Teargas rounds were fired from a police truck after a petrol bomb landed among police in riot gear, a Reuters witness said.
A female police officer was injured and skirmishes broke out between the leftist protesters and police, who used trucks to push back the crowd from near the EU Council building where Bush was meeting EU leaders. Two previous protests against Bush's visit on Sunday and Monday passed off peacefully with relatively small crowds.