Travis Dove for The New York Times
John Edwards left the Federal Courthouse in Greensboro, N.C. with daughter, Cate, during a break on Thursday.

GREENSBORO, N.C. — The jury in the federal campaign finance case against former Senator John Edwards said Thursday that it had found him not guilty on one of the six counts against him, and the judge declared a mistrial on the others.

The verdict came on the third count, which involved donations from the heiress Rachel Mellon. Mrs. Mellon gave more than $725,000 to help Mr. Edwards during his 2008 presidential campaign, during which large sums were spent to cover up an affair between Mr. Edwards and a former staff videographer, Rielle Mellon, with whom he conceived a daughter.
The third count involves a $200,000 check Mrs. Mellon wrote in 2008 as the Edwards campaign was collapsing. The check was not cashed until after the campaign had ended.
Earlier in the day, the jury sent a note to the court saying, “We have finished our deliberations and have arrived at our decision on counts one through six.”
But pressed in the courtroom by the judge, Catherine C. Eagles, the foreman said the jurors had reached a unanimous verdict on one count only. The verdict was not announced at that time.
The court, which had braced for what appeared to be a full verdict, appeared unprepared for the jury’s partial decision during the ninth day of deliberations.
Judge Eagles then sent the jurors out of the courtroom and asked each side how to proceed.
The prosecution recommended that the judge send the jury back to deliberate further. “The government’s view is it appears they are not finished,” said David Harbach II, the lead prosecutor.
Abbe Lowell, the head of Mr. Edwards’s legal team, noted that the jury had already taken twice as much time as the defense used to present its case and that deliberations had taken almost as long as the prosecution took. Mr. Lowell recommended that she accept the verdict on the third count and declare a mistrial on the rest.
Shortly after 3 p.m., the judge said she had decided to ask the jury to return to its deliberations for the afternoon.
Speaking before the jurors returned for her instructions, she said, “I want to make it clear to them they are not prisoners in there.”
Once the jurors had returned to the courtroom, she delivered what is known as an Allen charge, which essentially tells a jury that no other panel is likely to be as competent as this one in reaching a full verdict.
She said she knew that they had deliberated diligently, adding, “I do not intend to force any of you to abandon your deeply held views.”
About an hour later, the jurors returned and the one not-guilty verdict was announced. After considering how to proceed, the judge declared a mistrial on the other five charges.