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(CNN) —  

Rep. Beto O’Rourke said at a CNN town hall on Thursday that it’s a “definitive no” when asked if he foresees himself one day running for president.

O’Rourke, the Democrat challenging Republican incumbent Sen. Ted Cruz in Texas, has won progressive admirers across the country and shattered online fundraising records – fueling speculation that a presidential run could be in his future.

“The answer is no,” he said when asked if he foresaw a future presidential bid.

“Our children are 11, they’re 10 and they’re 7 years old. We’ve told them, we’re going to take these almost two years out of our life to run this race, and then we’re devoted and committed to being a family again. So that’s what we’re focused on,” O’Rourke said.

Pressed further by CNN’s Dana Bash, O’Rourke said, “It’s a definitive no.”

“Like never?” Bash asked.

“I mean, so – let me put it this way: I promise to you and most importantly to the people of Texas that I’ll serve every single day of a six-year term in the United States Senate and I won’t leave this state to go run for president,” he said.

If he doesn’t win the Senate race, he said, “we’re back in El Paso.”

CNN invited Sen. Ted Cruz multiple times to appear tonight in his own town hall, but he declined.