The U.S. government's chief defense and diplomatic officials were encouraged by the determination of Iraq's newly selected leader, but the itinerary on their second day of an unannounced visit underscored the difficulties ahead for U.S. forces and the emerging Iraqi government.

U.S. Defense Secretary Donald H. Rumsfeld began his day Thursday with a briefing on the latest programs and technologies to counter increasingly sophisticated roadside bombs that are a prime killer of U.S. forces in Iraq.

Rumsfeld and U.S. Secretary of State Condoleezza Rice later heard from U.S. diplomats advising Iraq's troubled Interior Ministry, which oversees security and police forces that are hobbled by corruption and riven by sectarian loyalties.

The double-barreled show of support from Rumsfeld and Rice for Iraq's first permanent democratic government was meant to resonate in Iraq and among Americans, whose frustration with the war effort has helped drive U.S. President George W. Bush's poll numbers to new lows.

Rumsfeld said the first step in regaining momentum after a four-month political deadlock in Iraq will be setting up and staffing competent government ministries and continuing to build stronger Iraqi security forces.

"The impression that the people of this country will have of the government will be the impression that Secretary Rice and I garnered from our meetings," Rumsfeld said Thursday.

"They are serious people and they recognize the difficulties of the task they are facing. They intend to get about he task of governing this country in a responsible way."

Rice called the new leadership determined and focused.

At a session with Rumsfeld on Thursday, Iraq's national security adviser, Muwaffak Rubaie, thanked Americans for sacrificing "money, sweat and treasure and blood" to help Iraq and spoke optimistically of substantial U.S. troop reductions this year and next. He did not mention specific figures.

U.S. officials have insisted there is no specific plan yet to reduce the size of the U.S. military presence in Iraq, although they have stressed that their aim is to gradually withdraw as Iraqi security forces become more competent and capable of fighting the insurgency.

Rubaie also spoke of U.S. troop reductions beyond this year.

"At the end of next year we would hope, or the next couple of years, we would hope that most of the coalition forces would go back home safely," he said. There are now about 132,000 U.S. troops in Iraq.

Rumsfeld, who addressed the meeting after Rubaie spoke, did not mention the subject of U.S. troop reductions, although he also spoke hopefully of the Iraqis taking more responsibility for their own security.

Rice and Rumsfeld held back-to-back sessions with Iraq's seven newly selected leaders Wednesday before having dinner at the residence of U.S. Ambassador Zalmay Khalilzad.

Khalilzad had pushed hard on the country's squabbling factions to resolve a four-month political stalemate that sapped Iraqi and U.S. confidence following the emotional high of successful Iraqi elections in December.

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 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.