A Democratic-leaning group announced on Monday the beginning of a seven-figure campaign to focus voter attention on the importance of the Supreme Court in the presidential election, with a heavy emphasis on the high court’s role in issues like abortion, gun safety and voting rights.

The group, Stand Up America, is kicking off the $1 million campaign on the second anniversary of the Dobbs v. Jackson decision, which overturned the right to an abortion and convulsed the country’s politics in its aftermath.

For years, Republicans have made the courts — especially the Supreme Court — a central issue in federal elections. The vacancy on the Supreme Court during the 2016 election was a central force behind Donald J. Trump’s victory. Among voters who said the Supreme Court was the “most important factor” in their decision, 56 percent cast a ballot for Mr. Trump, according to exit polls.

This year, Democrats are trying to harness that same energy: Though there is no current vacancy on the court, there is potential for a president to make appointments in the next administration.

With help from the actress Barbra Streisand and the TV host Andy Cohen, as well as social media influencers, doctors, lawyers, voters and politicians, the effort will include a website and a targeted digital ad campaign in presidential battleground states.

The goal, according to the group, is to raise awareness about the impact the election could have on the Supreme Court: Four of the nine justices, the group notes, will be in their 70s by 2025, giving the next president an opportunity to further shape a court that has become significantly more conservative since 2016.