Speaking after talks at the White House, both Blair and Bush pledged the US-led coalition would see Iraq through to a handover of political power to an interim government on June 30 and democratic elections in January 2005.
Shortly afterwards, the Arab television station Al-Jazeera aired footage showing a US soldier being held captive.
The soldier, dressed in camouflage, appeared unharmed and was shown sitting on the floor with a row of gunmen behind him.
The soldier, wearing a floppy desert hat, was seen speaking on the video, but his voice could not be heard.
Instead, a voiceover in Arabic said he was identifying himself as Pfc Keith Maupin.
Three Japanese nationals released on Wednesday after a week in captivity arrived in Dubai overnight for medical checks.
Tokyo said it had no more news about two more of its nationals reportedly abducted west of Baghdad on Wednesday.