Carrol, an advice columnist for Elle magazine, claims in an upcoming book about “hideous men” in her life that the US president forced himself on her in a changing room at New York’s Bergdorf Goodman department store in 1995 or 1996.
She describes a “colossal struggle” in which Mr Trump entered her “halfway – or completely, I’m not certain”.
Mr Trump insisted the incident “never happened” and that Carrol was “not my type”; a defence he has used against previous sexual assault allegations.
Republican senator Mitt Romney called for an “evaluation” into the claims, though he failed to make clear who should conduct it.
"Whether it's Congress or whether it's another setting, I'm not sure,” he told CNN on Wednesday. "It's a very serious allegation. I hope that it is fully evaluated. The president said it didn't happen and I certainly hope that's the case."
Joni Ernst, a Republican colleague of Mr Romney's said Carrol was right to come forward with the allegation.
"But obviously, there has to be some additional information. They need to interview her. They need to visit with him” she told CNN.
Many other Republicans, however, dismissed the allegation or claimed they were not even aware of it.
“He's denied it, and that's enough for me. Until somebody comes up with something new,” said Lindsey Graham, a Republican senator and one of Mr Trump’s closest allies in Congress.
Despite press coverage in print and on the airwaves, senator Marco Rubio told a reporter they were asking him “about a story that I’ve never even read”.
During the 2016 presidential campaign, more than a dozen women accused Mr Trump of sexual misconduct in earlier years. Mr Trump has denied the allegations and said the women are lying.
Carroll told CNN: “With all the 16 women who have come forward, it’s the same – he denies it, he turns it around, he attacks, and he threatens. Then everybody forgets it, and then the next woman comes along. And I am sick of it. We have to change this culture of sexual violence.”