Mr. Biden frequently discusses his family tragedies on the trail now, and did so during his run for president in the 2008 campaign. But he has not always been comfortable doing so, friends say. As recently as 2015, a Los Angeles Times report indicated that Mr. Biden considered a commercial that discussed the car accident to be treading on “sacred ground.” The group behind that spot, which was encouraging Mr. Biden to run for president, went on to say it would not televise that ad, and Mr. Biden did not seek the presidency the following year.

“For decades Joe did not talk on the campaign trail or in public events about the ways in which life really, you know, brought him to his knees, the loss of Neilia and his daughter and the ways in which those first couple of years were incredibly hard for him,” Senator Chris Coons of Delaware said in an interview in May, referring to Mr. Biden’s first wife. “In recent years he’s opened up a great deal more about it. And the equally tragic loss of his son Beau is something he’s turned into an opportunity to connect with the whole country.”

The new spot is not just about family tragedy; it is described by the campaign as a health care ad, touching on an issue that was critical to the Democrats’ victories in the 2018 midterm elections.

The commercial obliquely makes an argument Mr. Biden often advances more directly on the campaign trail: that his Democratic opponents who support “Medicare for all,” a single-payer health care system, are by default supporting the replacement of the Affordable Care Act, also known as Obamacare. Mr. Biden’s opponents say their goal is to further expand robust health care coverage.

As he often does, Mr. Biden highlights his relationship with former President Barack Obama to argue for expanding on the current health care law rather than pursuing a more sweeping measure. Emphasizing his partnership with Mr. Obama, a respected figure in the Democratic Party, has been a central strategy in Mr. Biden’s campaign.

“Health care is personal to me,” Mr. Biden says. “Obamacare is personal to me. When I see the president try to tear it down and others propose to replace it and start over, that’s personal to me too. We’ve got to build on what we did because every American deserves affordable health care.”

Last week, Mr. Biden released the first television ad of his campaign, called “Bones.” It highlighted his standing against President Trump in early polls and sought to paint Mr. Biden as best positioned to beat him in a high-stakes moment for the country, even as he has seen his lead over his rivals slip in some polls.