Dewhurst has overseen the Texas Senate from the powerful lieutenant governor's post since 2003 and has been endorsed by popular Gov. Rick Perry and much of the state's Republican establishment.
Cruz is the son of a Cuban immigrant who has a fiery public speaking style that has stirred up grassroots groups.
An Air Force veteran who also was stationed in Bolivia for the CIA, Dewhurst spoke Monday in San Antonio at one of the oldest Veterans of Foreign Wars posts in the country, flanked by Perry and Peter Holt, the owner of the city's NBA franchise, the Spurs.
Retired U.S. Navy fighter pilot Jake Ellzey spoke at the rally, telling the crowd, "I dare Ted Cruz to come in to any VFW post anywhere in the state and talk about fighting."
"Mr. Cruz, you're not a fighter because you've never worn the uniform," Ellzey said.
Asked if that was a fair assessment, Dewhurst said, "I agree with the commander."
"Normally, I've found in my life that the louder you speak, probably, the less of a fighter you are," he continued.
Cruz describes himself as the race's only true fighter for conservative values. A spokesman for his campaign, James Bernsen, said Monday that Ellzey's and Dewhurst's comments offended him as a veteran of the Iraq war.
"I find it offensive to make it a litmus test," Bernsen said. "Ted is very supportive of the military. But this is not something that should be politicized, period."
Associated Press writers Danny Robbins in Grapevine and Ramit Plushnick-Masti in contributed to this report.
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