Former President George W. Bush, visiting Washington to attend President Biden’s inauguration on Wednesday, privately told Representative James E. Clyburn, Democrat of South Carolina, that the congressman was “the savior” for helping Mr. Biden secure the Democratic nomination and defeat President Donald J. Trump.

“George Bush said to me today, he said, ‘You know, you’re the savior, because if you had not nominated Joe Biden, we would not be having this transfer of power today,” Mr. Clyburn told reporters on a call after the swearing-in ceremony on Wednesday. Mr. Clyburn’s endorsement of Mr. Biden in the Democratic primary in South Carolina in February was credited with rescuing a campaign that had faltered badly in Iowa and New Hampshire.

“He said to me that Joe Biden was the only one who could have defeated the incumbent president,” said Mr. Clyburn, who chatted with Mr. Bush on the inaugural platform before the ceremony and took a selfie with the former president.

Mr. Bush’s office did not dispute the comment but characterized it more as simple political analysis, not a statement of gratitude to Mr. Clyburn for saving the country from another term of Mr. Trump in the White House.

“This has been a bit overhyped,” said Freddy Ford, Mr. Bush’s chief of staff. “President Bush was acknowledging the congressman’s role in saving President Biden’s candidacy — nothing more, nothing biblical.”

Mr. Bush is no fan of Mr. Trump, who beat his brother Jeb Bush for the Republican nomination in 2016. That fall, the former president voted for “none of the above” rather than casting a ballot for Mr. Trump; his father, former President George Bush, voted for Hillary Clinton; his mother, Barbara Bush, wrote in Jeb’s name. The younger George Bush has not said publicly who he voted for in November, but few who know him think he voted for Mr. Trump.

At Mr. Trump’s swearing-in ceremony in January 2017, Mr. Bush was so struck by the new president’s dark Inaugural Address that he told Mrs. Clinton, “That was some weird [expletive].” He has since remained mostly silent, but his occasional public comments have been interpreted as rebukes of Mr. Trump’s approach to leadership.

Mr. Bush not only attended Mr. Biden’s inaugural ceremony on Wednesday but also traveled afterward to Arlington National Cemetery with the new president along with former Presidents Bill Clinton and Barack Obama to lay a wreath at the Tomb of the Unknowns. He also taped a segment with Mr. Clinton and Mr. Obama showed on television Wednesday night sending best wishes to Mr. Biden.

“Mr. President, I’m pulling for your success,” Mr. Bush said in the video. “Your success is our country’s success. God bless you.”