UNITED NATIONS—The United Nations is considering reopening its investigation into the mysterious 1961 plane crash that killed then-U.N. chief Dag Hammarskjöld after new evidence of possible foul play emerged.

The U.N. General Assembly put the case back on its agenda in March at the recommendation of Secretary-General Ban Ki-moon after more than half a century of speculation that the Swedish diplomat's plane was either sabotaged or shot down.

Mr. Ban's recommendation came after a report by the independent Hammarskjöld commission, formed in 2012 with the participation of South African jurist Richard Goldstone. The report in September raised the possibility the National Security Agency and other intelligence agencies have a tape-recorded radio communication by a mercenary pilot who allegedly carried out an aerial attack on the secretary-general's plane.

The NSA told the commission that none of its searches produced any account of the events surrounding the plane crash. But it added that "two NSA documents have been located that are associated with the event," which it has decided to withhold.

Mr. Hammarskjöld on his way to Northern Rhodesia—now Zambia—when his Swedish DC-6 airliner plunged into a forest 9 miles from the airport in the city of Ndola just past midnight on Sept. 18, 1961.