"Anything that would delay that or disrupt that as a result of turbulence or incompetence or corruption in government would be unfortunate," Rumsfeld said before he began a round of talks with Iraqi leaders.
The newly designated prime minister, Ibrahim al-Jaafari, told reporters after meeting Rumsfeld at his official residence that he realized the risk of setbacks in the political process.
"I don't deny there are challenges, but I am sure we are going to form very good ministries," he said in English. He predicted that the government bureaucracy would be staffed by "good technocrats" from a variety of backgrounds.
In other developments:
Rumsfeld met separately with Interim President Jalal Talabani, the Kurdish former rebel leader.
In a joint appearance before reporters after their meeting, Rumsfeld and Talabani struggled to make themselves understood to a mixed Iraqi-American press corps. At one point Talabani translated for Rumsfeld as the defense secretary fielded a question from an Iraqi speaking in Arabic. After hearing Talabani's version of the question, Rumsfeld accused the reporter of phrasing it inaccurately, and the garbled exchange ended abruptly as another Iraqi posed another question.
Speaking in English, Talabani said he had assured Rumsfeld that Iraq's interim leaders will work together.
"We are planning to have the (permanent) government as soon as possible, but you know this is the beginning of democratization in Iraq," Talabani said, adding that he expects the government to complete its selection of cabinet ministers before the end of this week. The next major goal is to have a new constitution written by August and ratified by a national vote in October.
Rumsfeld also held a closed meeting with Gen. George Casey and Lt. Gen. John Vines, the top two American commanders in Iraq. In a brief interview with reporters later, Casey said he was encouraged that the long and difficult process of training and equipping Iraqi security forces was gaining ground.
"We're getting better and more efficient at it," he said.
The Iraqis, in turn, have gained a new measure of confidence since the Jan. 30 elections.
"Iraqi security forces are operating more aggressively" against the insurgents, Casey said.
Thus a surge in attacks in early April is being matched by military successes, such as a string of nearly flawless weekend raids, CBS News Correspondent Lee Cowan reports. Overall the raids captured about 65 suspected insurgents.
But what makes the raids significant is the arrests were made by U.S.-trained Iraqi soldiers, not Americans themselves. This could be one of the reasons U.S. officials have indicated some of the U.S. force in Iraq could be coming home by early next year.
Rumsfeld also gave a pep talk to a few hundred soldiers at Camp Liberty, headquarters of the 3rd Infantry Division. He also pinned Bronze Star medals and Purple Heart awards on several soldiers and participated in a mass re-enlistment ceremony for about 100 soldiers gathered in a mess hall.
"The role you're playing is a critically important role in the global war on terrorism," he told them.
Rumsfeld arrived in the Iraqi capital before sunrise aboard an Air Force C-17 cargo plane for his second visit in three months. It was his ninth visit since the war began in March 2003.