Former Vice President Joseph R. Biden would be the choice of 39 percent of Democratic or Democratic-leaning voters if the party’s primaries were held today, a new CNN poll released Tuesday found.

That put him far ahead of the crowded field of candidates, and support for Biden appears to have increased after his official announcement last week. 

But the primaries will not be held today. A significant bloc of voters said they could still change their minds, and they want to know more about others in the field.

Among the 411 Democrats and Democratic leaners that SSRS, an independent polling firm, interviewed by phone between Thursday and Sunday, Sen. Kamala Harris of California topped the list of candidates voters want to hear more about.

Twenty-three percent of likely Democratic voters surveyed said they wanted to hear more about Harris, whom 5 percent said they would already vote for.

Twenty percent said they wanted to hear more about Sen. Elizabeth Warren of Massachusetts, who received top support from 8 percent of Democrats surveyed. Nineteen percent want to hear more about Biden; 17 percent about South Bend, Ind., Mayor Pete Buttigieg; and 15 percent about New Jersey Sen. Cory Booker and former Texas Rep. Beto O’Rourke.

Twelve percent of Democrats wanted to hear more about Sen. Bernie Sanders of Vermont.

Those numbers could prove important down the road. The first debate among Democratic candidates, when many voters may hear from all the candidates for the first time, will be in June.

“Only about a third of potential Democratic voters with a preference in the race (36 percent) say they will definitely back the candidate they currently support, [while] 64 percent say they could still change their minds,” CNN polling director Jennifer Agiesta wrote.

Biden has established himself as the clear front-runner and has received endorsements from a batch of high-profile politicians to complement that favorite status.

Sens. Bob Casey Jr. of Pennsylvania and Doug Jones of Alabama endorsed him soon after his announcement last week, as well as Reps. Tom Suozzi of New York and Matt Cartwright of Pennsylvania.  

Biden, who represented Delaware in the Senate for more than 30 years, also collected endorsements from the state’s entire congressional delegation: Sens. Chris Coons and Thomas R. Carper and Rep. Lisa Blunt Rochester. The endorsements made reference to decades of friendship and work alongside Biden, who won his first Senate election in 1972.

Other than Biden, Buttigieg is the only other candidate to receive a significant boost in his numbers compared to a CNN poll conducted in March. The South Bend Mayor, who has taken a tamer tone on anti-lobbyist rhetoric, received 7 percent support from potential Democratic voters in the latest CNN poll.

Eighty percent of the Democrats surveyed in the poll said they are satisfied with the current field of 21 major candidates who have announced bids so far.

NBC News will host the first presidential Democratic debate in Miami across two nights: June 26 and June 27.