Mr Abbott asked defence planners in May last year to examine the possibility of putting up to 12 of the short-take-off and vertical-landing F-35 Bs on to the two ships – the largest in the Navy – which carry helicopters and are likely to be primarily used to transport troops and equipment to war or disaster zones.
The first of the assault ships was completed last year and commissioned into the Navy in November as HMAS Canberra.
But defence officials conceded to a Senate estimates committee late last year that the jump-jet proposal would involve extensive modifications to the ships, including new radar systems, instrument landing systems, heat-resistant decking, restructuring of fuel storage and fuel lines, and storage hangars.
Defence sources have told The Australian Financial Review that the proposal was "still in the white paper mix" up until some weeks ago.
But one source close to the white paper was emphatic on Tuesday that "it will now not make the cut".
"There were just too many technical difficulties involved in modifying a ship which takes helicopters to take fighter jets and it is also very expensive," the source said. "You can safely say it has been dropped."
An F-35B Lightning II passes initial sea trials over the Atlantic.