WASHINGTON — Congressman George Santos positioned himself in a prime location for President Biden’s State of the Union address — an uncomfortably prominent place for the embattled new lawmaker who faces multiple investigations and has acknowledged embellishing and even lying about his life story.

Mr. Santos’ presence at the center aisle to see and be seen with the arrivals was met with a stern rebuke from a fellow Republican, Senator Romney.

“You don’t belong here,” the Utah Republican scolded Mr. Santos as he entered the House chamber and spotted the New York Republican on the aisle.

Words were exchanged, it was reported, though Mr. Romney said later he did not hear it all.

“He shouldn’t be in Congress, and they are going to go through the process and hopefully get him out,” Mr. Romney told reporters afterward, his office confirmed. “But he shouldn’t be there, and if he had any shame at all he wouldn’t be there.”

The exchange was an unusual lashing by the more reserved Mr. Romney, the Republican Party’s presidential nominee in 2012, but shows the discomfort Mr. Santos is bringing among traditional conservatives critical of the rightward drift of more extremist elements of the GOP.

Mr. Santos retorted with a tweet: “Hey @MittRomney just a reminder that you will NEVER be PRESIDENT!”

The arrival of Mr. Santos has been a problem for the Republicans since he won a New York congressional seat, which helped to deliver the party a slim majority, once his personal story began to unravel.

Mr. Santos has acknowledged fabricating, and at times lying, about parts of his education, work experience and even his family’s own religion and history.

Speaker McCarthy met privately with the congressman last week amid a swirl of potential investigations on and off Capitol Hill. Mr. Santos announced he would step aside from his committee assignments ahead of an expected House Ethics Committee probe.

Mr. McCarthy said Tuesday the situation with Mr. Santos would work its way through the House Ethics Committee. Fellow New York Republicans have called for Mr. Santos to resign from Congress. He faces other investigations beyond Congress.

Other Republicans heard the exchange and one Republican lawmaker who was told about it said there was widespread displeasure that Mr. Santos had situated himself in such a prominent spot. The lawmaker requested anonymity to discuss what others said about the subject.

The center aisle basically gave Mr. Santos the chance to seize the limelight by greeting the president and other prominent officials as they entered the House chamber and made their way down the aisle.

As senators entered the House in a line, it was then that Mr. Romney spotted Mr. Santos and delivered his message.

“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 told reporters later.

Mr. Romney said that given the investigations, Mr. Santos “should be sitting the back row and staying quiet, instead of parading in front of the president and people coming into the room.”

But Mr. Santos, as is often the case, had his moment, becoming for a time the face of the GOP.