President Joe Biden and Trump had a "substantive meeting and exchange of views" during their nearly two-hour Oval Office meeting on Tuesday, according to the White House press secretary.

"They discussed important national security and domestic policy issues facing the nation and the world," Karine Jean-Pierre told reporters during a briefing following the meeting. "President Biden also raised important items on Congress's to-do list for the lame duck session, including funding the government and providing the disaster supplemental funding the president requested."

Biden also reiterated that "we will have an orderly transition and a peaceful transition of power," she added.

On the national security discussion, ABC News Chief White House Correspondent Mary Bruce asked White House national security adviser Jake Sullivan if Biden made the case for the U.S. not to walk away from Ukraine, and how the message was received.

"I will only note that President Biden reinforced his view that the United States, standing with Ukraine on an ongoing basis, is in our national security interest," Sullivan responded, adding that "standing up to aggressors and dictators and pushing back against their aggression is vital to ensuring that we don't end up getting dragged directly into a war."

-ABC News' Molly Nagle

As Trump continues to round out his cabinet, the job of treasury secretary remains in flux, with the co-chair of Trump's transition team actively vying for the job, sources familiar with the matter told ABC News.

Howard Lutnick is looking to be tapped as treasury secretary, sources said, a move that comes as investor and hedge fund manager Scott Bessent is also a top contender for the role.

Bessent traveled to Mar-a-Lago as recently as Friday to meet with Trump about the job, the sources said.

Lutnick, on the other hand, spends hours with Trump nearly each day, presenting candidates for top roles in the administration. As such, the move by Lutnick to attempt to get a cabinet position for himself has frustrated some close to Trump.

Sources caution the job is still in flux and neither man could get the job -- with the potential for other candidates to emerge.

One potential dark horse for the job, one source told ABC News, is former Trump administration trade representative Robert Lighthizer, who Trump sees as an aggressive advocate for his tariff-heavy approach to international trade.

-ABC News' Jonathan Karl, Olivia Rubin and Katherine Faulders

President Joe Biden and Trump are meeting in the Oval Office, resuming a tradition that Trump himself flouted in 2020.

Biden spoke first and called for a smooth transition. Trump then said politics is tough but the transition will be smooth.

They did not answer questions.

Trump announced his senior staff on Wednesday, bringing back some of his well-known names from his first term and those who helped on his campaign.

Dan Scavino, one of Trump's long-time allies, was named assistant to the president and deputy chief of staff. Stephen Miller was named assistant to the president and deputy chief of staff, a move reported earlier this week.

James Blair, the Republican National Committee political director and campaign aide, has been named assistant to the president and deputy chief of staff for legislative, political and public affairs. Taylor Budowich will serve as assistant to the president and deputy chief of staff for communications and personnel. He was a senior member of several of Trump's PACs.