With about 55 percent of precincts counted in the Tucson-area district, Kelly had 37 percent in a four-way race, the Tucson Sentinel reported. Martha McSally, a retired Air Force pilot whose first run for office attracted national attention, was second with about 24 percent of the vote.
Kelly, an Iraq War veteran backed by the Tea Party, will be opposed by Ron Barber, a former Giffords aide. Barber was wounded in the 2011 shooting that left six people dead and Giffords with a major head injury.
A recent poll showed Kelly ahead of Barber by about 4 percentage points.
"We're going to work like we're down 10," he promised as he claimed the nomination at about 10 p.m.
Giffords, a moderate Democrat who has represented the district since 2006, remained in Congress during her months of rehabilitation at a Houston hospital. She resigned in January, saying she wanted to focus on her recovery.
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