Secretary of State Rice and Defense Secretary Rumsfeld praised the new Iraqi leadership in a joint visit to Baghdad, while saying that disarming militias would be a major task for the new government.

Ms. Rice told reporters late yesterday that the proposed Iraqi prime minister, Jawad al-Maliki, came across as “very focused” and “really impressive” in a meeting. Mr. Rumsfeld, speaking of the collective new Iraqi leadership, said, “It’s clear they have come to reasonable understandings about what the Iraqi people expect of them.”

The disbanding of sectarian militias is a “high priority” of the incoming Iraqi government, Ms. Rice said. Hundreds of Iraqis have been killed in attacks between the country’s Shiites and Sunnis.

The visits of the two major Bush administration Cabinet secretaries handling Iraq, so soon after Mr. al-Maliki’s selection as the prospective Iraqi leader, demonstrated the importance of his appointment toward enabling a handover of more security responsibility to the Iraqis.

Mr. al-Maliki told Ms. Rice and Mr. Rumsfeld he will work for cooperation among the country’s factions. “The end result of that will be something called Iraq,” he said, speaking through an interpreter. “This is going to be our work in the parliament for the next four years.”

The threat to Iraq’s stability was underscored yesterday when a video appeared on the Internet from a fugitive terrorist leader in Iraq, Abu Musab al-Zarqawi. He accused America of waging a “crusader” offensive and said the insurgency is standing firm against it.

President Talabani designated Mr. al-Maliki on April 22 as the proposed new Shiite prime minister, to begin the formation of a permanent government that will serve a four-year term. In addition to Mr. al-Maliki, Ms. Rice met Mr. Talabani, a prominent Kurdish leader; a Shiite and interim vice president, Adel Abdel Mahdi, and the head of the largest Sunni Arab political coalition, Tariq al-Hashemi.

With the formation of a new Iraqi government, the top American military commander in Iraq, General George Casey, said in Baghdad today that he remains on his “general timeline” for withdrawing some troops. He didn’t cite numbers.

The question of whether the American-led occupation of Iraq has been mishandled came up again in comments to reporters. Ms. Rice said America has “made errors” in Iraq and that history would judge the extent of those shortcomings.

“Have we made mistakes? I’m sure we have,” Ms. Rice told reporters in a joint press briefing with Mr. Rumsfeld in Baghdad after a day of meetings the two held with American and Iraqi officials.

Mr. Rumsfeld said the Pentagon “systematically” engages in a “lessons learned process” on Iraq.