(Adds police statement on missionaries) By C. Bryson Hull NAIROBI, Jan 27 (Reuters) - Carjackers armed with AK-47s shot dead two women in a U.S. embassy vehicle in Nairobi's western outskirts on Saturday, and police killed two of the fleeing gunmen during a shootout in the nearby bush. Police spokesman Gideon Kibunjah said two policemen were shot and wounded as they chased the gunmen after the midday carjacking on the main highway in the Kenyan capital, nicknamed "Nairobbery" by its residents. Gangsters driving a stolen vehicle had stopped in front of a black four-wheel drive with diplomatic plates issued to the United States and ordered the five occupants out, he said. "There was a person who was driving and an elderly lady who took too long to get out of the vehicle and the gangsters shot them and threw them out," Kibunjah said. "The two were confirmed dead on arrival at the hospital." Kenyan police said in a statement the victims were in a group of missionaries on their way to meet a friend. It was the fourth attack by criminals in Kenya in less than a year on diplomats or their families and the second involving the U.S. diplomatic community. A U.S. embassy spokeswoman said she could make no immediate comment. In Washington, a U.S. State Department official said he was aware of the report but had no details. COMMON CRIME Carjackings are common in Nairobi but are far more likely to occur at night, when attackers block roads and hold people up for their wallets, mobile phones and cars. In September, a U.S. embassy official was shot in the chest, while a month earlier the Russian ambassador was stabbed while on the roadside attending to a sick grandchild. A Danish diplomat's eye was gouged out in another attack. Television footage of Saturday's incident showed three white people -- an elderly man, a teenage boy and a woman -- standing at the scene. The two bodies had been covered. "They shot my sister and my mother," the woman said. An elderly Kenyan man, identified by residents as church elder Humphrey Mwaura Ruhang'a, wept and fell to the ground next to one victim. He told reporters: "They were my visitors." The driver of the first stolen vehicle was found at the scene, bound hand and foot in the back among potatoes spilled from a sack. "They took me while I was coming from prayers," the man, who identified himself only as a local pastor, told reporters. Soon after the fatal shootings, the gunmen dumped the diplomatic vehicle and its easily identifiable red plates. Kibunjah said it was a Toyota Land Cruiser Prado, a favourite target of carjackers in the east African country. Kibunjah said no arrests had been made yet but two AK-47s were recovered. Kenyan police, who patrol with assault rifles, generally give no quarter to armed criminals and shootouts are common. Internal Security Minister John Michuki last year issued a controversial "shoot-to-kill" order against armed criminals, many of whom have automatic weapons that have flooded Kenya for years from conflicts in neighbouring Somalia and Sudan. The shootings took place in Kinoo, a village-like western suburb of Nairobi on the road to resort towns like Naivasha favoured by city dwellers for weekend getaways. (Additional reporting by Robert Waweru in Nairobi and Deborah Charles in Washington)