The Prime Minister-elect tweeted his gratitude to the heads of state and government and other dignitaries since on Sunday. (Agencies)
"In our conversation, @BarackObama & I talked about further strengthening India-USA strategic partnership that will help both nations," he said in a tweet.
Obama had a few days ago called up Modi to congratulate him over his victory.
Modi has had an uneasy relationship with the US which denied him a visa in 2005 over 2002 Gujarat riots. He has, however, in his public utterances stressed that foreign relations cannot be "influenced" by incidents related to individuals.
Among others, Modi thanked leaders of Japan, Russia, Spain, Nepal, Canada, Germany and South Africa besides the UN Secretary General and the Dalai Lama.
"I thank President Putin for his good wishes. Looking forward to making our relations with Russia even stronger in the years to come."
"India-Russia friendship has stood the test of time. We will further strengthen our relations in a wide range of fields," he wrote in two tweets.
The Gujarat Chief Minister also mentioned Japan in his tweets speaking of his experience of working with the East Asian economic powerhouse.
"Personally, I have a wonderful experience of working with Japan as CM. I am sure we will take India-Japan ties to newer heights."
Thanking Nepal President Ram Baran Yadav and Prime Minister Sushil Koirala for their wishes, he referred to the neighbouring country as an "old & deeply valued friend".
In his tweets, he also thanked the prime ministers of New Zealand and Fiji for their good wishes.
The Prime Minister-elect tweeted his gratitude to the heads of state and government and other dignitaries since on Sunday.