TUCSON, Ariz. - An Iraq war veteran was leading a Republican primary in Arizona on Tuesday to pick a candidate for the seat of former Democratic Congresswoman Gabrielle Giffords, who was wounded in a shooting spree last year and later resigned.Jesse Kelly, the leading Republican candidate, narrowly lost to Giffords in the 2010 race that saw her elected to her third term to represent southeast Arizona, including part of Tucson.The winner of the primary held on Tuesday will compete in a June 12 special election against former Giffords aide Ronald Barber, who was also shot and wounded when a gunman opened fire on Giffords and killed six other people in January 2011.No one from Barber's Democratic party challenged him, and he has Giffords' endorsement.Kelly was leading with 37 percent of the vote compared to 24 percent for his closest rival, Martha McSally, with 55 percent of precincts reporting as of 10 p.m. local time, according to figures from the website of the Arizona Secretary of State.Kelly could not be reached for comment late on Tuesday.Kelly, a former Marine, works as a construction project manager. McSally is a former Air Force colonel who has flown over Iraq and Afghanistan and was the first American woman pilot to fly combat missions.The other two candidates, Arizona Senator Frank Antenori and sports broadcaster Dave Sitton, were running third and fourth respectively.Barber seized on the early voting totals to criticize his possible rival. "Kelly's priorities are the wrong priorities for Southern Arizona's middle class families and seniors," Barber said in a statement.Giffords' former district leans Republican, with 37 percent of voters registered Republican and 31 percent as Democrats, according to statistics from the website for the Arizona Secretary of State.Tom Volgy, a professor of government and public policy at the University of Arizona, said he expects Barber will win the special election in June and the later race in November, which will be held in a redrawn district to represent the area for a full two years in Congress.The shooting galvanized support for Giffords and her former aide, Barber, Volgy said. "That makes it a pretty clear case for Ron Barber winning the elections," he said.Giffords, a Democrat, stepped down in January to focus on her recovery a year after she was shot in the head at a congressional meet-and-greet event outside a Tucson supermarket.Jared Loughner, a 23-year-old college dropout, was charged with first-degree murder, the attempted assassination of Giffords and other crimes stemming from the shooting. He pleaded not guilty and was found mentally unfit to stand trial.