Dick Cheney, US vice-president, made a surprise visit to Baghdad on Monday as he kicked off an extensive tour of the Middle East in which he is expected to urge Saudi Arabia to increase oil production and step up pressure on Iran to rein in its nuclear programme.

He will also push for progress in the Middle East peace process, which has made little headway in spite of President George W. Bush’s high-profile tour of the region in January and a series of visits by Condoleezza Rice, US secretary of state.