Defense Secretary Donald Rumsfeld made a surprise visit to Iraq on Wednesday to hail the defeat of Saddam Hussein as fresh bloodshed erupted at an anti-American protest west of Baghdad. Residents of Falluja, 30 miles outside the capital where 13 people were killed in a rally late on Monday night, said U.S. troops shot dead two people during a demonstration on Wednesday. U.S. Major Michael Marti told Reuters that members of a convoy returned fire after shots were fired at them from a crowd outside a U.S. command post. He said soldiers counted "potentially" two injured Iraqis. Some local people believed as many as four people might have been killed and said the demonstrators had been unarmed. The bloodshed in Falluja provided a grim backdrop for the visit by Rumsfeld, who arrived in Baghdad after starting his trip in the southern city of Basra. In that city, Iraq's second biggest, he congratulated British troops who helped U.S. forces oust Saddam three weeks ago. "When one looks back on this effort, I think and pray that what will be significant is that a large number of human beings, intelligent and energetic, have been liberated," said Rumsfeld, the most senior U.S. official to visit Iraq since the war was launched on March 20. "They are out from under the heel of a truly brutal, vicious regime. And that's not only a good thing for them but it's a good thing for the region and the world." Rumsfeld was last in Iraq 20 years ago as an envoy of President Ronald Reagan . He held talks with Saddam as Washington sought to contain neighboring Iran, which Iraq had invaded in 1980. Senior U.S. military commanders were at Baghdad airport to greet Rumsfeld, who headed for a meeting with Jay Garner, the retired general in charge of American efforts to rebuild the country and launch a democratic government to replace Saddam's repressive reign. **ELATION GIVES WAY TO ANGER *** The elation that greeted the ousting of Saddam has quickly been replaced in many communities by increasingly angry demands for U.S. troops to go home and leave Iraqis to rule themselves. The bloodiest protests so far have been in Falluja, where witnesses said the unarmed demonstrators were killed when they marched on a school being used by U.S. troops as a barracks. U.S. officers said their men had opened fire in self-defense on Monday after members of the crowd shot at them. They estimated up to 10 people had been killed. In the latest shooting, a hospital official in Falluja said he had seen two young men who died of head wounds inflicted by U.S. troops on Wednesday. "The number of killed was two. They were hit in the head," said Ahmed al-Taha, putting their ages between the late 20s and early 30s. His hospital was treating eight wounded and other casualties were taken to a different clinic. Traveling unannounced and under tight security, Rumsfeld arrived in Iraq after a stop in Saudi Arabia where he announced that Washington was closing down the bulk of its military operations in the kingdom. The U.S. withdrawal ends a presence dating back to the 1991 Gulf War which sparked virulent opposition from Muslim groups offended by the presence of American troops in the home of Islam's holiest sites. The U.S. deployment was a key grievance of Saudi-born Osama bin Laden , whose al Qaeda group was blamed for the September 2001 attacks on the Pentagon and World Trade Center in which about 3,000 people were killed. President Bush cited the possibility that Saddam would provide al Qaeda with chemical and biological weapons as one of his reasons for going to war in Iraq. No traces of such weapons have yet been found, and members of the Saddam administration who are now in U.S. custody have reported that all weapons of mass destruction were destroyed before the war began. **IRAQI POLITICIANS TO MEET*** Rumsfeld was expected to see first hand how the reconstruction of postwar Iraq is progressing, although some towns and cities are still not fully under U.S. control. Leaders of Iraq's key political parties were due to meet in Baghdad on Thursday to discuss an interim authority for the country. A spokesman for the Iraqi National Congress (INC), Zaab Sethna, said the meeting would discuss a call for a national conference by late May to appoint an interim Iraqi authority. Two more senior members of Saddam Hussein's old guard were taken into American custody this week. U.S. forces said they were holding Saddam's veteran oil minister, Amir Muhammed Rasheed, whose wife is bioweapons scientist Rihab Taha, known as "Dr. Germ." Basra city governor Walid Hamid Tawfiq al-Tikriti -- a member of Saddam's inner circle -- gave himself up and was being questioned by U.S. officials in Baghdad, Sethna told Reuters. "He is somebody we believe should be investigated for possible involvement in crimes against humanity," he said. The United States now has 15 of the 55 most-wanted members of Saddam's administration in custody, although the fate of Saddam and his sons, Uday and Qusay, remains a mystery. **PHOTO CAPTION*** An Iraqi killed during an anti-U.S. protest is buried in a Falluja cemetery, 30 miles west of Baghdad, April 29, 2003. According to witnesses, U.S. troops shot dead at least 13 Iraqis during the protests. The bloodshed is sure to inflame anger at the U.S. presence in Iraq . Witnesses told Reuters the troops opened fire on unarmed demonstrators, but U.S. officers said their men returned fire after being shot at first. (Ruben Sprich/Reuters)