"Prime Minister Malcolm Turnbull and I spoke a short while ago. I congratulated him and conveyed best wishes," Modi said.
He said that he also thanked Turnbull for his birthday greetings to him.
Modi said he also spoke to outgoing Prime Minister Tony Abbott and appreciated his efforts in improving ties between India and Australia.
60-year-old Turnbull was made the Prime Minister after a hastily-arranged party leadership ballot on Monday night gave him 54 votes against 44 for incumbent Abbott.
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