Rice said U.S. officials were hearing "loud and clear" that the new Iraqi leadership intended to be nonsectarian in its decisions on who should head ministries, particularly Interior and Defense, which oversee police and armed forces respectively.
"I think they understand ... the importance of appointing ministers and subordinates who have a reputation for technical competence and a mind-set that is nonsectarian," Rice said.
Meanwhile, another sibling of Sunni Vice President Tariq Hashimi was slain in the country's continuing violence. Gunmen killed Maysoon Hashimi and a bodyguard this morning in Baghdad. Mahmoud Hashimi was shot to death April 13.
Tuesday, a civilian was killed by a roadside bomb near the city of Kirkuk, police said.
In the capital, a bomb on a bus exploded, killing four people and injuring 21.
In a western district of the city, two people were killed and four injured in a roadside bombing aimed at police.
Police also recovered 15 bodies from various Baghdad neighborhoods.
Just north of Baqubah, a roadside bomb exploded in the Shiite village of Kharnabat, killing three people and injuring 10, local police said.
The U.S. military announced that American-led forces killed a dozen suspected rebels during a raid Tuesday in Yousifiya.
Times staff writers Saif Hameed, Caesar Ahmed and Shamil Aziz in Baghdad and Johanna Neuman in Washington contributed to this report.