Trump inauguration live updates: Donald Trump moves swiftly to implement his new agenda

In more off-the-cuff remarks inside the Capitol's Emancipation Hall after his address, Trump spoke about people who have been convicted for their roles in the Jan. 6 attack on the Capitol as "hostages."

"I was going to talk about the J6 hostages," Trump said. "But you'll be happy because, you know, it's action not words that count."

Trump previously promised to pardon some Jan. 6 rioters on Day 1.

He also went after former Reps. Liz Cheney and Adam Kinzinger, two Republican members of the House Jan. 6 Committee who are outspoken critics of Trump because of his actions after the 2020 election.

"And I was going to talk about the things that Joe did today with the pardons of people that were, very, very guilty of very bad crimes, like the Unselect Committee of political thugs," Trump said.

Joe Biden, now the former president, left the Capitol on a Marine helicopter that will bring him to Joint Base Andrews for a final farewell to Washington.

The Bidens and Trumps walked together to the helicopter. Both couples were holding hands.

Biden smiled and appeared to laugh as he spoke to Trump. Jill Biden and Melania Trump hugged as they said goodbye.

This is an exit for Biden after five decades in politics.

Just before he left, Kamala Harris and Doug Emhoff entered their own motorcade. She is traveling home to Los Angeles, her office confirmed to ABC News.

A spokeswoman for the transition team says Donald Trump will order the renaming of the Gulf of Mexico and Alaska's Mount Denali in his first executive orders.

Spokeswoman Karoline Leavitt said on the social platform X that the Gulf of Mexico will be renamed the Gulf of America and Denali - the highest mountain in North America - will revert to Mount McKinley, its former name until the Obama administration changed it in 2015.

Trump will order a national energy emergency and issue orders aimed at the elimination of federal DEI programs, incoming officials say.

Earlier this month, Trump floated the idea of renaming the body of water that forms the coastline along five southeastern states, saying he felt "Gulf of America" has a "beautiful ring to it."

As president, Trump can take the action to rename the body of water, although other countries don't have to adopt the new name.

After Trump's speech, there were remarks from Rabbi Ari Berman, Pastor Lorenzo Sewell and Reverend Frank Mann. Christopher Macchio performed the national anthem.

Trump and Melania Trump left the Capitol Rotunda together.

Next, the Trumps will see off President Biden and Vice President Kamala Harris.