The two met Iraqi leaders, including Prime Minister-designate Nuri Kamil al-Maliki.
Afterward, Rumsfeld said he came away "most encouraged," while Rice described al-Maliki as "very focused."
Earlier, Rumsfeld said the future U.S. troop levels in Iraq would depend on the new government.
Al-Maliki, a Shi'ite, was chosen last week to head Iraq's government, formally ending a four-month deadlock among the country's Shi'ite, Sunni, and Kurdish groups.
The United States hopes a new national unity cabinet will help pull the country out of the insurgency and sectarian strife.
(compiled from agency reports)