SYDNEY, July 4 (Reuters) - Australia's surplus on trade goods narrowed in May as a rise in imports of fuel outpaced a pick up in iron ore exports, data showed on Thursday.

The Australian Bureau of Statistics reported the balance on goods narrowed to A$5.77 billion ($3.87 billion), from a downwardly revised A$6.0 billion in April and short of market forecasts of A$6.3 billion.

Exports rebounded by 2.8% in May led by gains in iron ore and transport equipment. Imports rose 3.9%, led by increases in fuel and cars.

($1 = 1.5186 Australian dollars) (Reporting by Wayne Cole; Editing by Christian Schmollinger)