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

Among executive orders signed by Trump at the Oval Office is one ending birthright citizenship.

Such a move, though, is expected to face significant legal hurdles. Under the 14th Amendment to the Constitution, any person born within the territory of the U.S. is a U.S. citizen.

When a reporter pointed out that that order will likely be challenged, Trump said, "You could be right."

"We have good grounds," he added.

Trump, surrounded by executive orders he planned to sign Monday evening, also signed an order pardoning approximately 1,500 Jan. 6 rioters.

The order also includes six commutations, he said.

"We hope they come out tonight. Frankly, they're expecting it," Trump told reporters.

As of early January, more than 1,580 individuals have been charged criminally in federal court in connection with Jan. 6, with over 1,000 pleading guilty, according to the Department of Justice.

Click here for a closer look at the sweeping pardons and commutations.

Elon Musk has been spotted at the White House West Wing, sources say.

Musk is said to have a blue badge -- which is essentially an all-access pass. Musk has office space in the Eisenhower Executive Office Building -- or the EEOB -- which is in the White House complex but situated next door.

Sources told ABC News that Musk is also likely to get West Wing office space.

Trump returned to the Oval Office to sign more executive orders at the Resolute desk, including one declaring a national emergency at the southern border.