The British prime minister has said he agreed with the US president that there were "duties to discharge and responsibilities to keep'' in Iraq.
At a joint news conference at Camp David on Monday, Gordon Brown said: "Our aim, like the United States is, step-by-step, to move control to the Iraqi authorities.''
George Bush and Brown, who were meeting for the first time since Brown became prime minister, also touched on Iran, Afghanistan, Darfur, terrorism and the importance of climate change.
Brown hinted that a decision about troops levels would be made soon, while assuring they would be based "on the military advice of our commanders on the ground".
He also said that Britain's and the US's aims in Iraq included "security and political reconciliation".
Iran sanctions
On Iran, the two leaders agreed the next step is toughening sanctions through another UN resolution over the country's nuclear programme.
Brown said: "We're in agreement that sanctions are working and the next stage we are ready to move towards is to toughen the sanctions with a further UN resolution."
Bush told Brown: "I appreciate very much British commitment in Afghanistan…''
Pressure on Sudan
Bush and Brown also agreed they would "step up" pressure to end violence in Sudan's Darfur province.
Brown said: "I've agreed with the president that we step up our pressure to end the violence that has displaced two million people, made four million hungry and reliant on food aid, and murdered 200,000 people.
"We're agreed on expediting the UN resolution for a joint UN-African Union peace force. We're agreed on encouragement for early peace talks, a call to cease violence on the ground, an end to aerial bombing of civilians, and support for economic development if this happens and further sanctions if this does not happen."
On Tuesday, Brown will hold talks in New York with Ban Ki-moon, the UN's secretary-general, and give a speech at its headquarters.