MADRID, Dec 5 (Reuters) - Spain could seek the extradition of three U.S. soldiers after its Supreme Court said on Tuesday it had reopened a murder investigation into the killing of Spanish cameraman Jose Couso during the Iraq invasion. The Supreme Court overturned a decision earlier this year by a lower tribunal to close the case brought by Couso's family, who had requested the arrest of the three soldiers, a court spokesman said. Couso, a cameraman for Spain's Telecinco television station, was killed when a tank fired a shell at the Palestine Hotel in Baghdad on April 8, 2003. Reuters cameraman Taras Protsyuk was also killed and three other Reuters employees seriously injured. The lower court had ruled Spain did not have jurisdiction over what the family's suit described as a "war crime" but the Supreme Court disagreed. Couso's family celebrated the latest ruling but recognised it would be difficult to obtain the extradition of Sergeant Thomas Gibson, Captain Philip Wolford and Lieutenant-Colonel Philip De Camp. "We know it's going to be tough and that the United States, unfortunately, doesn't pay much attention to international law," Couso's brother, Javier, told Spanish national radio. "The courts of our country, although it's just a medium-sized power, a small power, will ask them with dignity to explain what happened on April 8," he said. The United States acknowledged the tank fired on the Palestine Hotel but cleared the soldiers of any blame. The New York-based Committee to Protect Journalists criticised the Pentagon report on the incident, saying it failed to address the question of "why U.S. troops were not aware that the Palestine Hotel -- one of the best-known civilian sites in Baghdad at the time -- was full of journalists."