CHAPEL HILL, North Carolina (CNN) -- Former Sen. John Edwards announced Thursday he has no plans to suspend his campaign for the Democratic presidential nomination due to his wife's recurrence of cancer.

"The campaign goes on," he said, contradicting earlier media reports to the contrary.

"You can go cower in the corner and hide or you can go out there and stand up for what you believe in," he said. "We have no intentions of cowering in the corner."

A biopsy of a tumor found on Elizabeth Edwards' rib showed "the cancer has returned, it was malignant," he said.

"We are very optimistic about this," he said, noting that the tumor is small in size and has a "relatively minimal presence."

Elizabeth Edwards underwent treatment for breast cancer after the 2004 campaign, in which her husband was the Democratic vice presidential nominee.

Her cancer was believed to be in remission.