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Tucson, Arizona (CNN) -- First, Daniel Hernandez heard the shots ring out. Then he heard someone yell, "Gun!"

Moments later, he was at Rep. Gabrielle Giffords' side. Less than a week after the 20-year-old intern started working for the congresswoman, he was using his bare hands to stop blood gushing from where a bullet had entered her head.

Hernandez, who trained as a certified nursing assistant, said he lifted Giffords' head to make it easier for her to breathe, then applied pressure to her wound.

"She was alert and conscious, but she wasn't able to speak, so the way she was communicating was by grabbing my hand and squeezing," Hernandez said.

Employees from the nearby Safeway supermarket brought out clean smocks from the meat department to cover Giffords' wound until paramedics arrived, he said.

"My main thing was just to keep her as alert as possible and just keep trying to interact with her. ... The entire time I was with the congresswoman, she was still responding," Hernandez said. "She was obviously in a lot of pain, so I let her know to squeeze my hand as hard as she needed to."

She "was my first and only priority," Hernandez added later in a CNN interview. I was "trying to take care of her emotional needs" and "keep her calm."

After the ambulance arrived, Hernandez rode with her to the hospital.

As details emerged about Saturday's shooting and its aftermath, praise poured in for Hernandez's role.

"I just really think he's one of the heroes here, because I think it's possible that his swift thinking and his training is what saved her life," said state Rep. Steve Farley of Arizona.

But Hernandez said it was Giffords who deserved recognition.

"People have been referring to me as a hero. I don't think that I am. I think the people who are heroes are people like Gabby, who have dedicated their lives to public service," he said. "It just makes me happy to know that I could help her in any way that I could."

Giffords "is known for being a fighter," he added. "She's going to pull through."

CNN's Alan Silverleib contributed to this report.