The documents show the NSA also tracked journalists from the New York Times and the Washington Post and two senators.
Some NSA officials later described the programme as “disreputable if not outright illegal”, the documents show.
The operation, dubbed “Minaret”, was originally exposed in the 1970s.
However, the names of those on the phone-tapping “watch list” had been kept secret until now.
The secret papers were published after a government panel ruled in favor of researchers at George Washington University.
The university’s National Security Archive – a research institute that seeks to check government secrecy – described the names on the NSA’s watch-list as “eye-popping”.
The NSA eavesdropped on civil rights leaders Martin Luther King and Whitney Young as well as boxing champion Muhammad Ali, New York Times journalist Tom Wicker and Washington Post columnist Art Buchwald.
The agency also monitored the overseas phone calls of two prominent US senators – Democrat Frank Church and Republican Howard Baker.
Many of those targeted were considered to be critics of US involvement in the Vietnam War.
In 1967 the strength of the anti-war campaign led President Lyndon Johnson to ask US intelligence agencies to find out if some protests were being stoked by foreign governments.
The NSA worked with other spy agencies to draw up the “watch lists” of anti-war critics, tapping their phone calls.
The programme continued after President Richard Nixon entered the White House in 1969. US Attorney General Elliot Richardson shut down the NSA programme in 1973, just as the Nixon administration was engulfed in the Watergate scandal.
The latest revelations come as the NSA is embroiled in fresh controversy over its surveillance programmes.
US intelligence leaker Edward Snowden recently exposed far-reaching electronic surveillance of phone records and internet traffic by the agency.
Researchers Matthew Aid and William Burr, who published the documents on Wednesday, said the spying abuses during the Vietnam War era far surpassed any excesses of the current programme.
“As shocking as the recent revelations about the NSA’s domestic eavesdropping have been, there has been no evidence so far of today’s signal intelligence corps taking a step like this, to monitor the White House’s political enemies,” they wrote.
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