Washington, along with European powers, boycotted the 63-year-old for a decade and denied him a visa over religious riots that erupted in 2002 during his tenure as chief minister of Gujarat state.
Kerry tweeted congratulations to Modi on Friday after a landslide win for his Hindu nationalist Bharatiya Janata Party, saying he looked forward to "growing shared prosperity/security".
President Barack Obama telephoned Modi, a keen user of social networks, but is yet to comment in person. He had warm words for his predecessor on Saturday, however.
As Manmohan Singh left office after 10 years in power in New Delhi, Obama called to tell him that there were "very few people in public life that I have admired or appreciated more".
Modi has displayed no rancour publicly about his treatment by Washington, telling an interviewer earlier this month that foreign relations "should not and cannot be influenced by incidents related to individuals".
But analysts are looking closely at how the world's biggest democracies embrace each other with Modi in charge and following a highly damaging spat over the arrest of an Indian diplomat in New York in December.
Modi, writing on Twitter to his 4.2 million followers, addressed a message to Russian President Putin on Monday saying that he looked forward "to making our relations with Russia even stronger in the years to come."
Japanese premier Shinzo Abe meanwhile was thanked for his good wishes, as were the leaders of Spain, Germany and France.
"Personally, I have a wonderful experience of working with Japan as CM (chief minister). I am sure we will take India-Japan ties to newer heights," Modi wrote on Monday.
Spokespeople for Modi and colleagues in his Bharatiya Janata Party either declined to comment or were unable to speak when contacted by AFP.- US 'at disadvantage' -
With the West boycotting him, Modi made repeated trips to East Asia and diplomats say Modi may pay an early visit to Japan to meet Abe, a fellow nationalist elected on a platform of economic revival.
Modi was chief minister of Gujarat in 2002 when anti-Muslim riots broke out, leaving about 1,000 people, mostly Muslims, dead.
Although he has never been found guilty of wrongdoing, the failure of his administration to control the violence left a legacy of suspicion.
He was refused a visa to the United States in 2005.
US officials "are painfully aware that they are at a real disadvantage by not having a relationship with Modi or really knowing him," Milan Vaishnav of the Carnegie Endowment for International Peace told AFP.
"They are going to try to remedy that as quickly as possible."
Britain also boycotted Modi, but British Prime Minister David Cameron sent a message of congratulations on Friday which was acknowledged by Modi the day after.
"Hoping to further strengthen India-UK relations," he wrote.