Nato ambassadors meeting in the Turkish city of Istanbul have reached a draft agreement to provide training for Iraq's armed forces.
Halting the violence in Iraq is the top priority
The move follows a request from interim Iraqi prime minister Iyad Allawi.
Details of how the training will be provided have not been revealed, but the plan is expected to be approved at the alliance summit starting on Monday.
But a BBC correspondent says this is a far cry from Mr Bush's original desire for Nato to send troops to Iraq.
The BBC's Tim Franks in Istanbul says although the alliance has responded positively to the Iraqi interim government's request for training and equipment what the agreement will amount to in practical terms remains unresolved.
It took hours of negotiations even for the Nato ambassadors to agree the abstract wording of the pledge, our correspondent says.
The meeting of the leaders of the 26 Nato member states is aimed at resolving differences over Iraq, Afghanistan and the long term future of the alliance.
The US and UK governments are pushing for the fullest possible Nato involvement in Iraq.
Before US President George W Bush arrived in Turkey for the two-day summit, he received general support from European Union leaders at a meeting in Ireland.
He said they had agreed to put aside any past differences over Iraq, and co-operate on economic reconstruction.
Before leaving Ireland, Mr Bush said: "Nato has the capability and... the responsibility to help the Iraqi people defeat the terrorist threat facing their country".
France, Germany and Belgium are more cautious over Nato involvement in Iraq, having strongly opposed last year's invasion.
But the draft agreement allows even some of Washington's sternest critics to take part.
"I am confident here in Istanbul we will give the final approval," Nato Secretary General Jaap de Hoop Scheffer said.
But the talks may clouded by the news that suspected al-Qaeda militants have kidnapped three Turkish men in Iraq.
The use of Nato troops in Afghanistan will also be discussed
In a message broadcast on al-Jazeera television on Saturday, militants claiming to be supporters of senior al-Qaeda member Abu Musab al-Zarqawi threatened to behead the men after 72 hours if all Turkish companies do not withdraw from Iraq.
Observers say shoring up international support for the US presence in Iraq is a goal of the Bush administration, which faces presidential elections in November.
Domestic opinion polls show declining support for the Iraq occupation, as a succession of deadly bomb attacks overshadow the planned transition of power.
Mr Bush's trip to Europe comes just days before the 30 June handover.
At the end of the US-EU meeting in Ireland the leaders issued a joint statement saying Baghdad needed the world's backing if Iraq was to become a democratic nation.
"The bitter differences over the [Iraq] war are over," Mr Bush said during a joint news conference with Irish Prime Minister Bertie Ahern and outgoing European Commission President Romano Prodi.
The Nato summit will also discuss the alliance's work in Afghanistan, where it has a contingent of peacekeeping troops.
Our correspondent says there will be a similar tussle among member states over extending Nato's remit there, all of which will lead to continuing questions about the long term health of the transatlantic alliance.