Rumsfeld said before a round of talks with Iraqi leaders, the Associated Press reported, "Anything that would delay that (the formation of a new government) or disrupt that as a result of turbulence or incompetence or corruption in government would be unfortunate."
Newly named 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, according to the AP. He predicted that the government would be staffed by "good technocrats" from a variety of backgrounds.
Rumsfeld met separately with interim President Jalal Talabani, the Kurdish former rebel leader.
Talabani said in English that 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 the government will likely complete its selection of cabinet ministers before the end of the week.
The interim government also plans to have a new constitution written by August and ratified by a national vote in October.
Rumsfeld also met with two of the top American commanders in Iraq -- Gen. George Casey and Lt. Gen. John Vines -- in closed-door sessions.
Casey told reporters that he was encouraged that the long and difficult process of training and equipping Iraqi security forces was gaining ground, reported the AP.
"We're getting better and more efficient at it," he said.
During his visit, Iraqi security forces said they had captured a senior former member of the Baath Party, Fadhil Ibrahim Mahmud al-Mashadani, who was believed to have planned and funded several insurgent attacks, Reuters reported.
Also on Tuesday, Poland said it would pull its troops from Iraq by the end of the year, citing improved stability in Iraq and the mission's high cost to Polish taxpayers.
The announcement, which made official an earlier proposal, prompted accusations that that the government was trying to garner favor among voters ahead of elections likely to take place in September.
Poles have been less critical of the Iraq war than other Western nations, but some of the government's nationalist and populist rivals have made the Iraq pullout a campaign issue.
Poland is among Washington's most loyal European allies and sent 1,700 soldiers to Iraq -- the fourth largest contingent beside U.S. troops after Britain, South Korea and Italy, according to Reuters.