BAGHDAD, April 26 (Reuters) - The United States’ diplomatic and military chiefs both flew in to Baghdad on Wednesday to meet Iraq’s new prime minister, emphasising the importance Washington attaches to his success in forming a national unity government.

Secretary of State Condoleezza Rice and Defense Secretary Donald Rumsfeld arrived separately and were to meet Prime Minister-designate Jawad al-Maliki together later, a day after al Qaeda in Iraq leader Abu Musab al-Zarqawi released a video condemning the government as a puppet of the United States.