Rumsfeld has so far held talks with the top U.S. commander in Iraq, General George Casey. After the meeting, Rumsfeld stressed the importance of the new Iraqi government, calling the formation of the "first government that doesn't have a qualifier in front of [its name] ... another important milestone."
"This is a sovereign government, and they are making impressive progress," he said.
Rumsfeld also said the number of U.S. troops stationed in Iraq in future will depend on the government being formed by Prime Minister-designate Jawad al-Maliki.
The Pentagon chief also said he and Casey had discussed engaging the new government in talks about the division of security responsibilities between U.S. and Iraqi troops.
Casey said the selection of senior government leaders marked a "major step" toward creating conditions that could allow a substantial number of U.S. troops to leave.
Rumsfeld is scheduled to meet al-Maliki and a number of other Iraqi leaders.
On April 25, al-Maliki called for the country's militias to be disarmed, saying they threaten to push the country into civil war.
Al-Maliki urged Iraq's Shi'ites, Kurds, and Arab Sunnis to unite against suicide bombings, shootings, and assassinations.
(compiled from agency reports)