Sydney and Melbourne property prices rebounded in June after a pullback the month before, but there remains signs the national market was cooling as regulators tightened the screws on leveraged property investors.

Property consultant CoreLogic said its index of home prices for the combined capital cities rose 0.8 per cent in June, following a rare 1.1 per cent drop in May. Sydney and Melbourne drove the June increase, rising by 2.8 per cent and 2.2 per cent respectively.

Hobart (+2.8 per cent) and Canberra (+2.6 per cent) while Perth 9+1.4 per cent) was in positive territory but Darwin (-2.2 per cent) Adelaide (-1.7 per cent) and Brisbane (-0.5 per cent) went backwards.

Annual price growth in Sydney ran at 12.2 per cent in June, down from a top of 18.9 per cent in March. Melbourne fared better, with prices up 1.5 per cent in the June quarter and 13.7 per cent for the year.