The centerpiece of the unprecedented Rice-Rumsfeld joint visit was their first meeting with Nouri al-Maliki, selected last week as a compromise candidate for prime minister to break the sectarian logjam. He has a month to form a new government that the United States hopes will pave the way for eventual U.S. withdrawal.

Al-Maliki was largely unknown outside Iraq before his selection, but both Rice and Rumsfeld said they found him impressive and focused on fixing Iraq's grinding problems.

Al-Maliki opposed both Saddam Hussein and the U.S.-led invasion that overthrew the dictator more than three years ago. He has been described as a hardline Shiite partisan and by U.S. officials as an Iraqi patriot who stood up to attempted political meddling by neighboring Iran.

"We know that he's not always agreed with us, or we with him," Rice said. "But he is somebody who has always had the interests of the Iraqis at heart and who has worked hard on their behalf."

Neither Rice nor Rumsfeld had met Al-Maliki before Wednesday's joint session with him. Rice met with him a second time privately.

Rice said the United States must be ready to help the new leaders take advantage of the fresh opportunity the new government represents. Many of her sessions with Rumsfeld focused on buttressing the government in its first 100 days.

She left behind a senior aide, Jim Wilkinson, to help al-Maliki organize his staff and operations.

The secrecy surrounding the two leaders' visit and the omnipresent security precautions inside the fortified U.S. government complex underscored the dangers and difficulties the Iraqi leaders inherit.

Shortly before they left the country Thursday, a sister of Iraq's new Sunni vice president, Tariq al-Hashimi, was killed in a drive-by shooting as she was leaving her home in southwestern Baghdad, said police Capt. Jamel Hussein.

It was the second killing in al-Hashimi's immediate family in two weeks. On April 13, his brother, Mahmoud al-Hashimi, was shot dead while driving in a mostly Shiite area of east Baghdad.

Rumsfeld was headed back to Washington early Thursday and Rice was flying to Bulgaria for a gathering of NATO foreign ministers.

Two-thirds of Americans now say the disapprove of Bush's handling of Iraq in AP-Ipsos polling earlier this month.

The administration remains under election-year pressure from the public and many in Congress to draw down its forces there, but Rumsfeld said Iraqi leaders did not raise the subject with him.

Army Gen. George Casey, the top U.S. military commander, said selection of government leaders marked a major step toward creating conditions that could allow a partial withdrawal.

"I'm still on my general timeline" for a possible withdrawal, he told reporters after meeting with Rumsfeld.

Casey used no figures. There are about 130,000 U.S. troops in Iraq, and military officials have spoken before of their hopes of reducing that number below 100,000 by the end of the year if the insurgency does not grow worse and if Iraq makes continued progress on political and security fronts.

Bush said last month that some U.S. troops could stay in Iraq for years.