But then, on Tuesday, her press secretary appeared to walk back the first lady's dual invitation.
Biden watched LSU's 102-85 victory over Iowa from the stands at American Airlines Center in Dallas on Sunday night.
Speaking Monday at the Colorado state Capitol in Denver, she praised Iowa's sportsmanship and congratulated both teams on their performances.
"I know we'll have the champions come to the White House; we always do. So, we hope LSU will come," she said. "But, you know, I'm going to tell Joe I think Iowa should come too, because they played such a good game."
After LSU's victory, Tigers coach Kim Mulkey said she would go to the White House if the team was invited.
LSU star Angel Reese tweeted a link to a story on Jill Biden's remarks Monday. "A JOKE," she wrote, along with three rolling-on-the-floor-laughing emojis.
The first lady's press secretary, Vanessa Valdivia, took to Twitter on Tuesday to clarify, saying that Jill Biden "admires how far women have advanced in sports since the passing of Title IX" and that "Her comments in Colorado were intended to applaud the historic game and all women athletes. She looks forward to celebrating the LSU Tigers on their championship win at the White House."
Also on Tuesday morning, President Biden tweeted that he's looking forward to welcoming the women's NCAA champions to the White House with no mention of Iowa.
"Congrats to @LSUwbkb who demonstrated excellence on and off the court. They showed us what it looks like to win with an unrelenting belief in themselves. And they did it in one of the most-watched women's sports games in US history. You have an incredible school, @LSUpresident."
Reese -- the Final Four's Most Outstanding Player -- has gotten a lot of attention on social media during the past 24 hours, ever since she waved her hand in front of her face while staring down Iowa star Caitlin Clark in the final moments of LSU's win, then pointed toward her finger as if to say a ring was coming.
Clark set the record for points scored in an NCAA tournament with 191 in six games. If she saw Reese's gestures, Clark didn't seem concerned about them.
Social media lit up in the aftermath, with some saying it was trash talk that is just part of the game, while others condemned Reese for lacking grace in victory. Reese was unapologetic.
"All year, I was critiqued about who I was," Reese said. "I don't fit in a box that y'all want me to be in. I'm too hood. I'm too ghetto. But when other people do it, y'all say nothing. So this was for the girls that look like me, that's going to speak up on what they believe in. It's unapologetically you."
Reese is Black, and Clark is white.
Clark made a similar face-waving gesture to no one in particular during Iowa's Elite Eight victory over Louisville.
Iowa coach Lisa Bluder and Clark on Tuesday both said that Iowa didn't earn a trip to the White House, and Bluder instead issued an open invitation for Jill Biden to visit the Hawkeyes' program.
I gratefully acknowledge the First Lady's sentiments, but a day at the White House should belong solely to the champion, LSU and Coach Mulkey. We would welcome the First Lady and President to come to Iowa's "House" - Carver Hawkeye Arena - any time!— Lisa Bluder (@LisaBluder) April 4, 2023
Said Clark to SportsCenter: "I don't think runner-ups usually go to the White House. LSU should enjoy that moment for them. And congratulations, obviously; they deserve to go there. Maybe I could go to the White House [someday] on different terms."
In her remarks, Jill Biden also marveled at how far women's sports in the United States have come since Title IX in 1972 gave women equal rights in sports at schools that receive federal funding.
"It was so exciting, wasn't it? It was such a great game" she said. "I'm old enough that I remember when we got Title IX. We fought so hard, right? We fought so hard. And look at where women's sports have come today."
Information from The Associated Press contributed to this report.