Biden, President Barack Obama's vice president, apologized for the first time Saturday for comments he made weeks ago about working with segregationists in Congress during the 1970s.
"I've been doing this rodeo far too long," Obama said in response to King's question about the tiff. "And no comment."
The former first lady also said she and her husband would not be endorsing any candidate from the crowded field, saying they would support whomever wins the primary.
"Barack and I are going to support whoever wins the primary, so ... our primary focus is letting the primary process play out, because it's very early," she said. "I mean, that's one of the things that we learned in the campaign. It is early; it's like trying to figure out who's winning the World Series on the first seven games. I mean that's where we are right now, it is so early."
Barack Obama had previously said he did not intend to endorse his former vice president early. And Biden said he asked the former president not to.
"I didn't want it to look like he was putting his thumb on the scale," the former vice president told "The View" in April.
While staying mostly out of current politics, Michelle Obama did manage to take a not-so-subtle jab at the man now in the White House.
"The leader of the free world, with a tweet, can start a war, can crush an economy, can change the future of our children," she said. "It is a real job which requires deep seriousness and focus."
She has criticized President Donald Trump before and said in her recent memoir, "Becoming," she will never forgive him for the birther controversy he helped to perpetuate in the years prior to his campaign.
But Michelle Obama spent much of her time on stage at the Mercedes-Benz Superdome discussing voting rates among African Americans and urging those in attendance to get to the polls next year.
"I fear that sometimes people might have thought that Barack made it look easy, so it must be easy, It's kind of like, I guess, if the black guy can do it, anybody can do it. And that's not true," she said to laughs from the mostly African American crowd.
She closed with a message of motivation for the crowd.
"I feel the power in the Superdome right here," she said. "I feel it. I feel it right now. If each of us does our part and we go out there and we get educated and we register and we get people registered to vote. We can change things."
ABC News' Mark Osborne contributed to this report.