The "Sicario" actress appeared on the Today show and apologised for her verbal gaffe, reported People magazine.
"It was so not the intention to hurt anybody or cause any offense, so I really apologise to those that I caused offense," she said.
"It was just an offhand joke. I think I'll probably leave the political jokes to late night or something."
Blunt, 32, said the first GOP debate scared her after becoming a citizen.
Blunt also feels becoming the citizen was special to her.
"It's really meaningful. You know, I mean, my two favourite people in the world are American - my husband (John Krasinski) and my daughter. It was kind of a special day.