BAGHDAD, Feb. 17 -- Secretary of State Condoleezza Rice made an unannounced visit to Baghdad Saturday and publicly hailed early signs of success in a U.S.-Iraqi operation to quell sectarian violence in the embattled capital. But she cautioned that longer-term prospects would depend on how the Iraqi government uses its "breathing space" to promote political reconciliation and economic progress.

Rice, the highest-ranking U.S. official to visit Iraq since the start of the new crackdown, told reporters after a meeting with Iraqi Prime Minister Nouri al-Maliki and other top officials that she was "very impressed with the leadership of the prime minister and his team." She added, "Thus far we believe that they're clearly showing that this can be a new phase for the people of Iraq."

She also said the operation was bringing "a new hope and a new optimism" to Baghdad, and she expressed satisfaction with the level of participation by Iraqi army units. Pentagon officials previously had said the Iraqi units being deployed for the crackdown were at 45 percent to 55 percent of their troop strength, which they said was not sufficient. But Rice said Saturday that commanders informed her the troop strength now was as high as 90 percent.

While Rice did not voice any public reservations about the security operation, she told Maliki that it needs to "rise above sectarianism" and noted that no U.S. or Iraqi forces have yet moved into Sadr City, a teeming Shiite Muslim neighborhood in eastern Baghdad, the Associated Press reported. Sadr City is a stronghold of the Mahdi Army, a Shiite militia that is headed by firebrand anti-American cleric Moqtada al-Sadr and has been accused of using death squads to retaliate against Sunni Muslims for insurgent attacks. Sunni Muslim political leaders have complained that their sect's neighborhoods have been targeted in the security operation while Shiite strongholds so far have been spared.

Quoting an official familiar with the talks between Rice and Maliki, whose administration is dominated by fellow Shiites, AP said the Iraqi side argued that Sadr has been cooperating with authorities on security issues lately and that the government should not "waste our resources on a place that's stable."

The U.S. military and the Iraqi government, meanwhile, announced Saturday that the Baghdad security operation has been dubbed "Fardh al-Qanoon," an Iraqi phrase that means "Enforcing the Law."

"The plan is imposing the law on anyone who violates it," Maliki said, according to a U.S. military press release.

Rice's stopover, part of a Middle East trip that includes meetings with Israeli and Palestinian leaders, gave her a first-hand view of the Baghdad security operation, which is considered crucial to U.S. efforts to contain the violence in Iraq. Because of military action in the capital, Rice's plane circled the Baghdad airport for half an hour before coming in for a landing, news agencies reported.

Although killings have decreased since the start of the operation in Baghdad three days ago, a double car bombing in the northern city of Kirkuk killed at least 10 people and wounded 60 Saturday in a crowded market. Police reported that a suicide bomber detonated his explosives-laden vehicle moments after a booby-trapped car exploded in a predominantly Kurdish area of the ethnically mixed city.

Rice told reporters accompanying her that U.S. and Iraqi troops are "off to a good start" in implementing the Baghdad security plan, which she noted "was not ever intended to be a single day, but to ramp up over time."

But she cautioned that long-term success will depend on how the Iraqi government uses any period of relative calm resulting from the crackdown on rampant sectarian violence.

"If, in fact, militias decide to stand down and stop killing innocent Iraqis . . . that can't be a bad thing," Rice said. "But how the Iraqis use the breathing space that that might provide is what's really important."

Shortly after her arrival, Rice held a town hall-style meeting with U.S. Embassy and military personnel in the heavily fortified Green Zone.

In a pep talk to about 250 Americans at the former Iraqi presidential palace that now houses the U.S. Embassy, Rice alluded to a debate taking place in the United States over the war in Iraq. In Washington, the Senate is holding a rare Saturday session to consider a nonbinding resolution, passed by the House Friday, that expresses disapproval of President Bush's plan to send 21,500 additional troops to Iraq to help carry out the Baghdad security operation and reinforce Anbar province.

"Some do not think this war was the right war to fight," she said. "Some believe we in the administration haven't fought it quite right." But she told the diplomats and service members gathered in a spacious palace lounge that the work they are doing is "noble" and "necessary." Rice thanked them for their "sacrifice" and assured them that "it's appreciated across the board."

After her meeting with Maliki, Rice told reporters, "Some of the debate in Washington is in fact indicative of the concerns that some of the American people have for the prospects of success if the Iraqi government doesn't do what it has said it will do." She expressed hope that the security clampdown may give "a little bit of a spur" to Iraqi efforts to meet political and economic benchmarks.

Among the officials accompanying her was Karen P. Hughes, a longtime Bush confidant who currently serves as undersecretary of state for public diplomacy and public affairs.

Rice was scheduled to fly to Israel this weekend for a meeting with Israeli Foreign Minister Tzipi Livni, and she planned to hold talks Monday in Jerusalem with Israeli Prime Minister Ehud Olmert and Palestinian President Mahmoud Abbas.

Her visit came amid a relative lull in violence, which the Iraqi government held up as a promising sign that the new Baghdad security plan is off to a good start. A top U.S. military official sounded a more cautionary note, saying the capital might be experiencing a temporary respite as militant organizations assess the new measures and gear up to fight back.

Maliki assured President Bush Friday that the three-day-old plan "has achieved fabulous success," according to an account of the conversation released by the prime minister's office. Speaking by secure video link-up, Maliki also told Bush that officials will be "firm in dealing with any side that breaks the law, regardless" of their sect.

U.S. Maj. Gen. Joseph F. Fil Jr., the commander of the 1st Cavalry Division in Baghdad, spoke of the recent calm in more cautious terms. "We do expect there are going to be some very rough, difficult days ahead," Fil told reporters at the Pentagon Friday, speaking from Baghdad in a video link-up, according to a transcript. "This enemy knows how -- they understand lethality, and they have a thirst for blood like I have never seen anywhere before."

Meanwhile on Friday, a U.S. military spokesman said the leader of a powerful Sunni insurgent group in Iraq was not wounded in a clash with police, denying a report from Iraq's Interior Ministry. "We believe that al-Masri was not killed or wounded in any action yesterday," Lt. Col. Christopher C. Garver said Friday.

A ministry spokesman said Thursday night that the leader of al-Qaeda in Iraq, who is known by the alias Abu Ayyub al-Masri, was injured in a shootout with police earlier that evening. The spokesman also said one of Masri's top deputies, Abu Abdullah al-Mujamie, was killed in a gun battle with police near Samarra.

A statement posted online attributed to the insurgent group denied that Masri had been killed and accused the Iraqi government of fabricating the report.

However, an al-Qaeda in Iraq leader confirmed the death of the deputy in a phone interview Thursday night. Repeated attempts to reach ministry sources Friday for further details on the reported clash were unsuccessful.

Iraqi and U.S. forces have been sweeping targeted areas of the city to root out insurgents and restore order in neighborhoods. So far, officials say, they have met little resistance.

The increased patrols are accompanied by other security measures, such as tightened controls at the borders with Syria and Iran and a crackdown on civilians carrying weapons.

To support the growing number of U.S. Army brigades in the Baghdad area, Pentagon officials said Friday that an additional division headquarters of about 1,000 soldiers will be sent three months earlier than expected. The 3rd Infantry Division headquarters, based at Fort Stewart, Ga., will deploy to Iraq in March instead of June. The soldiers will provide command and control, intelligence, surveillance and reconnaissance.

The acceleration of the deployment reflects an immediate need for more support for what will be 10 U.S. brigades in Iraq's capital, officials said. There are currently eight brigades operating under the 1st Cavalry Division's leadership.

The deployment is the headquarters' third to Iraq, including the initial invasion of Baghdad in 2003. The unit's original June deployment was announced in November and was scheduled to be part of President Bush's plan to send about 17,500 additional U.S. troops to Baghdad.

Branigin reported from Washington. Staff writer Josh White in Washington and special correspondent Waleed Saffar in Baghdad contributed to this report.