Prosecutor Pedro Rubira said in his appeal: "Spain lacks jurisdiction to investigate causes of death in a military conflict and death of a Spanish citizen resulting from US military gunfire."
Rubira also said in his appeal that the three men have not been indicted, as the case is still in an early phase, the court official said on Thursday on customary condition of anonymity.
Thursday's motion was an appeal to National Court Judge Santiago Pedraz, who on Wednesday issued the warrant for Sergeant Shawn Gibson, Captain Philip Wolford and Lieutenant-Colonel Philip de Camp - all from the US 3rd Infantry, based in Fort Stewart, Georgia.
Jose Couso, who worked for the Spanish television network Telecinco, died on 8 April 2003 after a US army tank crew fired a shell on Hotel Palestine in Baghdad, where many journalists were staying to cover the war.
Reuters cameraman Taras Protsyuk, a Ukrainian, was also killed.
Pedraz had sent two requests to the US - in April 2004 and June 2005 - to have statements taken from the suspects or to obtain permission for a Spanish delegation to question them. Both went unanswered.
Couso's family with the warrant
issued by a Spanish judge
He said he issued the arrest order because of a lack of judicial cooperation from the US regarding the case.
The warrant "is the only effective measure to ensure the presence of the suspects in the case being handled by Spanish justice, given the lack of judicial cooperation by US authorities", the judge said in the warrant.
The Pentagon had no immediate information and said it was looking into it.
US officials have insisted that the soldiers believed they were being shot at when they opened fire.