A twin bombing left 11 dead in northern Iraq Saturday and US aircraft struck Sunni insurgents west of Baghdad, as Iraqi officials claimed early success in the campaign to restore order in the capital. US Secretary of State Condoleezza Rice paid an unannounced visit to Baghdad on Saturday to discuss the security crackdown. She urged the Iraqis in a private meeting to "rise above sectarianism" and pursue Shiite as well as Sunni extremists, an Iraqi official said. Rice also told Iraqi government leaders that the contentious debate in Washington over US President George W. Bush's war strategy reflects US doubts that democracy will prevail over violence. "Some of the debate in Washington is in fact indicative of the concerns that some of the American people have ... if the Iraqi government doesn't do what it has said it will do," Rice said she told leaders from all of Iraq's factions. The bombers struck in a Kurdish neighborhood of the oil city of Kirkuk, about 290 kilometers north of Baghdad, as streets were filled with cars and pedestrians on the main shopping day of the week. Police and witnesses said the first blast occurred near shops and a bus depot. Minutes later, a suicide car bomber attacked the same area. The back-to-back lasts shattered about 20 shops as terrified shoppers fled screaming in panic amid burning cars and debris. A total of 11 people were killed in the two blasts and 65 were wounded, police Brig. Gen. Sarhat Qader said. Sunni Arabs and Kurds have laid rival claims on Kirkuk and its vast oil wealth. In Ramadi, a Sunni insurgent hotbed 110 kilometers west of the capital, US jets strafed gunmen with 40mm machine gun fire after they ambushed a US patrol with small arms and rocket-propelled grenades, a Marine spokesman 2nd Lt. Roger Hollenbeck said. Hours later, US aircraft used precision weapons to destroy a car with gunmen who were trying to escape after they attacked a US Army patrol with small arms fire, Hollenbeck said. There were no US casualties, but Hollenbeck said eight insurgents were killed - four in each attack. The attacks north and west of the capital contrasted with a lull in major violence in Baghdad as US and Iraqi forces try to regain control from sectarian militias and criminal gangs. Some US officers believe Sunni and Shiite extremists have fled Baghdad to avoid the crackdown, citing an increase in attacks in provinces that border the city. The US military said Saturday that a Marine was killed the day before during combat operations in Anbar province, which includes Ramadi. It was the first US death reported since Wednesday when five soldiers were killed - all but one of them in Diyala province northeast of Baghdad. Iraqi authorities said they foiled a would-be suicide attack near Karbala, about 80 kilometers south of Baghdad. A minivan came under fire after the driver failed to slowdown at a checkpoint, and then detonated the explosives and was killed in the blast, said Karbala police spokesman Rahman Mishawi. There were no other casualties. In Baghdad, however, much of the gunfire appeared to come from Iraqi police firing weapons in the air to clear the way for their convoys speeding through the city. Police and soldiers searched cars at the numerous checkpoints. On Palestine Street, a main thoroughfare in east Baghdad, police commandos with armored personnel carriers manned dozens of checkpoints - some only about 100 meters (yards) apart. In Waziriyah, a Sunni area of northeast Baghdad, cranes set concrete blast barriers into place to block would-be suicide bombers. American paratroopers from the US 82nd Airborne Division joined Iraqi soldiers in a sweep through a mostly Sunni neighborhood in the center of the capital. US Apache helicopters flew overhead, and a US jet streaked low across the sky in a show of force. Although the Baghdad operation has been in full-swing only four days, Iraqi authorities have already begun heralding it as a major success. Iraqi spokesman Brig. Gen. Qassim Moussawi told reporters that "crimes and terrorist attacks" had dropped by 80 percent since the long-awaited security operation began in force last Wednesday. Police said the bodies of only five apparent victims of sectarian death squads were found in Saturday across the capital - in contrast to the scores that were recovered daily in the weeks before the crackdown. US officials, however, have been more cautious, saying it's too early to declare success. But Sunni politicians have complained that the initial raids have focused on Sunni neighborhoods, sparing Shiite hotspots such as Sadr City, stronghold of the Mahdi Army of anti-American cleric Muqtada al-Sadr. Sunnis blame the Mahdi Army for much of the sectarian violence which has rocked Baghdad for nearly a year and for forcing thousands of Sunni families from their homes. Shiites insist the greater threat comes from Sunni extremists including al-Qaida in Iraq. Al-Sadr is a close ally of Prime Minister Nouri al-Maliki. The Shiite prime minister convinced al-Sadr to remove many of his armed militiamen from the streets to avoid a showdown with the Americans. But many Sunni politicians believe al-Maliki is still reluctant to sanction a major military operation against al-Sadr's followers in the capital. During a private meeting with Iraqi leaders, Rice said the Shiite-led government must "rise above sectarianism" and noted that no US or Iraqi forces have yet moved into Sadr City, according to an Iraqi official familiar with the discussions. The Iraqis, however, told her that the Mahdi Army and al-Sadr had been losing influence and were cooperating with authorities on security issues, the official said. The Iraqis said they did not want to "waste our resources in a place that's stable," the official added. The official spoke on condition of anonymity because he is not authorized to release the information to the media. He said Rice stopped short of accusing the Iraqis of displaying pro-Shiite bias in the operation and said it appeared that the crackdown was going well. Documents captured during a raid about a month ago show that al-Qaida in Iraq has a carefully planned strategy aimed at downing coalition aircraft using a variety of weapons, said a US defense official, who spoke on condition of anonymity because of the sensitivity of the information. The official said the documents provide fresh evidence that the al-Qaida insurgency is adapting and posing new threats to US forces. The contents of the seized materials were summarized in an intelligence report analyzing recent helicopter crashes. The New York Times, which first reported on the intelligence analysis, said militants want to concentrate on air forces. In the last month, at least six US helicopters have gone down; five of the crashes were blamed on hostile ground fire. The deadliest was a Black Hawk hit by small arms fire on Jan. 20, killing all 12 soldiers aboard. On Feb. 2, Gen. Peter Pace, chairman of the Joint Chiefs of Staff, acknowleged that ground fire has been more effective against US helicopters recently.