Inside the tense exchange between Romney and Santos.

WASHINGTON — It began on the floor the House, in an impromptu but strikingly testy exchange just before the State of the Union address.

Senator Mitt Romney, the Utah Republican known for his party-bucking stands and emphasis on moral rectitude, could be seen scolding Representative George Santos, the New York freshman who faces multiple investigations after fabricating much of his résumé.

Mr. Romney admonished Mr. Santos for positioning himself in a prime camera-ready spot in the chamber, saying he didn’t belong there, and had no shame.

“I didn’t expect that he’d be standing there trying to shake hands with every senator and the President of the United States,” Mr. Romney said afterward to reporters who asked about the incident, which was captured on camera and erupted on social media.

He added: “Given the fact that he’s under ethics investigation, he should be sitting in the back row and staying quiet instead of parading in front of the president and people coming into the room.”

After the tense exchange between the two Republicans, the usually cheerful Mr. Santos looked slightly stung, and then annoyed. The hostile encounter stood out in a sea of lawmakers, glad-handing and happily greeting one another.

The Utah Republican, in his remarks to reporters, did not hold back, calling Mr. Santos “a sick puppy” who should resign — a position that puts Mr. Romney at odds with Speaker Kevin McCarthy of California and the House leadership. Among the falsehoods put forward by Mr. Santos are assertions that he worked at Goldman Sachs, graduated from college, had grandparents who fled the Holocaust and a mother who escaped from the World Trade Center on Sept. 11, 2001.

Mr. Romney told reporters such statements are not merely exaggerations.

“He says he, you know, that he embellished his record. Look, embellishing is saying you got an A when you got an A-. Lying is saying you graduated from a college that you didn’t even attend and he shouldn’t be in Congress.”

The encounter was in many ways vintage Romney, who was one of the few Republicans to vote for impeaching President Donald J. Trump and has not shied from defying his party’s base. A one-time bishop in the Church of Latter Day Saints, Mr. Romney, 75, often frames his positions in deeply moral terms.

“He shouldn’t be in Congress,” Mr. Romney said. “If he had any shame at all, he wouldn’t be there.”

Still, the moment was also vintage Santos, who appears to enjoy nothing more than attention and was determined not to give Romney the final word, offering a final taunt on Twitter.

Shortly after the speech ended, Mr. Santos tweeted at Mr. Romney, the party’s failed 2012 presidential nominee, that he would never make it to the White House.