Rumsfeld said political intrigue and nepotism could spark "lack of confidence or corruption in government".
He said the United States also opposed any move to delay the political schedule in Iraq, which includes drafting a new constitution by mid-August and national elections in December.
"The presence of US security forces is not going to be something that is going to go on forever," he told reporters travelling with him aboard his military transport plane on a flight from Washington.
Carrying a clear message from the US administration, Rumsfeld said he would hold talks in Baghdad with Iraq's new interim Prime Minister Ibrahim al-Jafari and interim President Jalal Talabani.
Despite al-Jafari and Talabani's designation as major figures in the new transitional government last week, political factions in Iraq continue to actively jockey for power.
Rumsfeld said decisions such as government appointments in ministries should be for the good of Iraq and not based on party loyalties or retribution.
"It's important that the new government be attentive to the competence of the people in the ministries and that they avoid unnecessary turbulence," he said.
"We have an opportunity to continue to make progress politically, economically ... anything that would delay that or disrupt that as a result of turbulence, or lack of confidence or corruption in government, would be unfortunate."