Prime Minister Tony Abbott has congratulated his newly elected Indian counterpart on a resounding victory and invited him to visit Australia.

Prime Minister Tony Abbott has invited his newly-elected Indian counterpart to November’s G20 summit in Brisbane.

Mr Abbott called Indian prime minister-elect Narendra Modi on Friday night to congratulate him on a resounding victory.

After a marathon six-week election for the world’s biggest democracy, hardline Hindu nationalist Mr Modi is on track for the first parliamentary majority by a single party in 30 years.

Mr Abbott told Mr Modi he was looking forward to working with him.