Former Vice President Joseph R. Biden Jr. joined forces with his top surrogate Thursday morning, releasing a video of a conversation with former President Barack Obama that cast the current occupant of the White House as unworthy and Mr. Biden as the perfect leader to replace him.

Mr. Biden and Mr. Obama covered several topics in the wide-ranging, 15 minute conversation, including President Trump’s faltering response to the coronavirus pandemic, health care, economic recovery, police brutality and presidential leadership.

The conversation, recorded at Mr. Obama’s Washington, D.C. office, was “socially distanced,” as Mr. Biden continues to contrast himself with Mr. Trump, who has only halfheartedly embraced coronavirus mitigation tactics such as wearing face masks and staying six feet away from another person. Mr. Biden and his former boss entered the office wearing masks, as the former vice president continues to diverge with Mr. Trump on that issue, then the two men sat in chairs across a room, not wearing masks, as they discussed how Mr. Biden would govern as president.

The video, coming at a time when Mr. Biden is leading Mr. Trump in the polls, was part interview and part political layup, with Mr. Obama teeing up Mr. Biden to talk about current events in the lens in which he was most comfortable. The two men repeatedly circled back to Mr. Trump, drawing a contrast with how Mr. Obama’s administration — and Mr. Biden’s potential White House — would handle situations differently than the incumbent.

Mr. Trump has been “deliberately dividing people from the moment he came down that escalator,” Mr. Biden said. “And I think people are now going, ‘I don’t want my kid growing up that way.’”

Mr. Obama responded by saying, in part, “The thing I’ve got confidence in, Joe, is your heart and your character, and the fact that you are going to be able to reassemble the kind of government that cares about people and brings people together.”

The video was released Thursday at 10 a.m. and represents another careful step into the political arena by Mr. Obama, who is desperate to see Mr. Trump defeated but for months remained behind the scenes as he sought to let the Democratic Party chart its own course. Hours ahead of the release, Mr. Biden’s campaign released several clips online, which built anticipation and showed Mr. Obama’s wide reach as a campaign surrogate and a highly respected leader of the Party.

At one point the two men discussed the importance of health care, referring to the Affordable Care Act the Obama Administration passed early in its first term. Mr. Biden talked about on it in deeply personal terms, reflecting on the death of his son, Beau, from brain cancer.

That experience, Mr. Biden told Mr. Obama, underscored the importance of the health care legislation.

“I used to sit there and watch him in the bed and in pain and dying of glioblastoma,” Mr. Biden said of his older son, who died in 2015. “And I thought to myself, what would happen if his insurance company was able to come in, which they could have done before we passed Obamacare, and said: ‘You’ve outrun your insurance. You’ve outlived it. Suffer the last five months of your life in peace. You’re on your own.’”

Health care was a central issue for Democrats in the 2018 midterm elections, and they are emphasizing it again this election cycle, especially with the pandemic underscoring the importance of insurance coverage and care for the sick.

Mr. Trump came into office on a promise to repeal the Affordable Care Act, but he and Republicans in Congress failed in their efforts to undo the health law in 2017. Still, the Trump administration has repeatedly sought to undermine the law, and it is now asking the Supreme Court to overturn it.

“You and I both know what it’s like to have somebody you love get really sick, and in some cases to lose somebody,” Mr. Obama told Mr. Biden in their conversation. He called the Affordable Care Act a piece of “starter house” legislation, giving Mr. Biden room to tout his proposed public health insurance option that would build on Mr. Obama’s efforts.

“But that loss is compounded when you see the stress on their faces, because they’re worried that they’re being a burden on their families. They’re worried about whether the insurance is going to cover the treatments that they need.”

In another portion of the conversation, which was released on Wednesday, the two talked about their response to the Black Lives Matter movement and the current protests for racial equality. During Mr. Obama’s administration, some activists criticized the president for blocking efforts at systemic reform but there is large agreement he was more receptive than Mr. Trump.

Mr. Obama, the country’s first Black president, touted the police accountability measures implemented in his administration, including tasking the Justice Department with police oversight. He cited some instances of overt racism that still persist, including job discrimination.

“This is a process we’re all going through, and we’re all learning,” Mr. Obama said. “And something I’ve always admired about you Joe is your willingness to listen and to learn. It is a sign of leadership when you’re willingness to hear other people’s experiences.”

The two are planning another online fund-raiser next week, with tickets ranging from $250 to $250,000. The Obamas, both the former president and his wife, Michelle, are likely the most high profile endorsers that Mr. Biden has, with the ability to drive attention and fund-raising unlike any other Democrats.

That Democrats have nominated his former vice president gives Mr. Obama a special entrance point to this election cycle, but he was rarely far away. During the primary, several candidates branded themselves as their heir to the “Obama coalition,” which could help Democrats achieve in 2020 what they failed to achieve in 2016.

The topics discussed in the video also function as a cheat sheet to the Biden campaign’s political message ahead. of the general election. Mr. Obama ended the video talking about how Mr. Biden’s “basic decency” was just as important as any political message.

The two men also spent time focusing on the failures of Mr. Trump in responding to the coronavirus pandemic and the financial devastation it caused.

“You can’t separate out the public health crisis from the economy,” Mr. Obama said. “If you want the economy growing, people have to feel safe.”

Mr. Biden responded: “What you did, and what all great presidents do, is persuade.”