"This result underlines the huge anger among Junior Doctors at the staffing turmoil and years of pay decline they have been subjected to," HCSA President Dr Naru Narayanan said in a statemnt.
The union said they will now agree the timing and shape of strike action "in coordination with other health unions."
HCSA is a smaller hospital doctors' union, with many represented instead by the larger British Medical Association.
(Reporting by Farouq Suleiman, editing by Andy Bruce)