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.