Reuters reported that Diamond said Devon Energy and Murphy Oil had declared force majeure on two of its rigs.
Cobalt International Energy made public its declaration on another Diamond rig last month.
Diamond said it rejected all these claims, especially in light of a judge's ruling against the moratorium last week.
"We are currently in discussions with these operators in this regard," Diamond said in its latest rig status report.
The US government expects to announce a revised moratorium in the next few days.
Because of the deepwater moratorium and tighter regulation of all US drilling in response to the BP oil well blowout, Gulf of Mexico rig operators face a number of force majeure claims, which can let companies out of contractual obligations due to events beyond their control.
The Ocean Endeavor is earning about $290,000 per day from Devon on a four-year contract running through June next year, and the Ocean Confidence is earning some $510,000 per day from Murphy on a four-year contract to February 2012. Cobalt had the Ocean Monarch through early August at $440,000 per day.
Diamond said the Monarch was then due to resume its original contract with Anadarko Petroleum, which analysts say is one of three contracts Anadarko has sought to escape via force majeure, along with two others with Transocean and Noble Corp.
Reuters reported that it was not immediately clear whether the status of the dispute with Anadarko had changed, and officials from Anadarko and Diamond were not immediately available to comment.