Newly-released documents claim the singer sent messages from his Miami home to London lawyers Haymon and Walters, with one telegram reading: "What you have done is just about the limit. I have taken out a contract ... it is now a question of time."
The firm reported Robin - who married Molly, the mother of two of his children, in 1968 and divorced in 1980 after years living separate lives - to the FBI after receiving "numerous threatening telegrams from Gibb which threatened their lives", according to the bureau's report.
Files released under the Freedom of Information Act show investigators considered further action and discussed how to probe the allegations without alerting the 'Staying Alive' hitmaker, who was at the height of his fame.
However, Robin's lawyers wrote to the FBI and said the singer "would not be foolish enough to carry out any threat, especially in view of his singing career".
The matter was eventually dropped, with the file closed in March 1981 because Molly and the lawyers did not want to press charges.