Columbia, S.C. ? The late Sen. Strom Thurmond’s family has accepted a California woman’s claim that she is the illegitimate mixed-race daughter of the one-time segregationist.

“We have no reason to believe Ms. Williams was not telling the truth,” Strom Thurmond Jr. told The (Columbia) State for a story in today’s editions.

Essie Mae Washington-Williams, 78, broke a decadeslong silence this weekend to say she was the daughter of Strom Thurmond and a 16-year-old maid working in his father’s home.

Thurmond Jr. said he would like to meet the retired Los Angeles schoolteacher sometime, preferably in private, to establish a relationship.

Earlier Monday, Thurmond’s family released a statement acknowledging Williams’ claims.

“As J. Strom Thurmond has passed away and cannot speak for himself, the Thurmond family acknowledges Ms. Essie Mae Washington-Williams’ claim to her heritage. We hope this acknowledgment will bring closure for Ms. Williams,” the family’s lawyer, J. Mark Taylor, said.

Williams is glad to see the matter resolved, said her lawyer, Glenn Walters. “Mrs. Essie Mae Washington-Williams can now take a place in history as a daughter of U.S. Sen. Strom Thurmond,” Walters said.

Thurmond died in June at age 100.

Williams had long been rumored to be Thurmond’s child, though she previously denied it. She finally came forward at the urging and encouragement of her children.

Williams said Thurmond privately acknowledged her as his daughter and had provided financial support since 1941. She said she waited to go public because she didn’t want to embarrass herself or hurt Thurmond’s career. The Washington Post first reported her claims on its Web site Saturday.

Williams said Thurmond fathered her when he was 22 and living in his parents’ home in Edgefield. Her mother, Carrie Butler, 16, worked as a maid in the Thurmonds’ home.

Raised by an aunt, Williams told the Post she first met Thurmond around 1941, when she was 16, and Thurmond called her a “very lovely daughter.”