Belafonte filed papers Tuesday in federal court in New York seeking the release of the memorabilia from Sotheby's, The New York Times reported. The auction house has had the items in storage since 2008 when the King children challenged his ownership and halted a sale.
The documents are an outline for a 1967 speech on Vietnam, written in Belafonte's apartment, a condolence letter from President Lyndon Johnson to Coretta Scott King after the civil rights leader was assassinated, and an envelope found in King's pocket after his death.
Belafonte said all King memorabilia he holds was given to him, while the children said in 2008 the items now at Sotheby's were part of a "wrongfully acquired collection."
"The papers are symbolic," Belafonte told the Times. "It's really about what happened to the children, and I feel that somewhere, in this one area, I really failed Martin."
Belafonte had a close relationship with King, sometimes helping support his family.
King's heirs have been involved in litigation over his papers. Coretta King tried and failed in the 1980s to get Boston University to return thousands of documents her husband donated in the 1960s, and in 2011 the estate disputed the ownership of documents held by one of King's former secretaries, losing again.
Belafonte's lawyer said the children, Dexter, Berenice and Martin Luther King III, have missed the deadline for filing a lawsuit to claim ownership of the documents. Belafonte said he had planned to donate the proceeds of the sale to Barrios Unidos, a charity combating urban violence.