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Since taking office on Friday, President Trump has not yet called leaders of the UK, German, Russia or China. PM Modi was dialled ahead of them, but after the heads of neighbouring countries like Mexico and Canada.
PM Modi and President Trump are both working to ensure improved and expanded relations between the US and India are not affected by the change in the White House.
After his election, PM Modi built a strong rapport with Barack Obama who became the first sitting US president to pay a second visit to India during the 2015 Republic Day celebrations.
During the call, President Trump emphasised that the United States "considers India a true friend and partner in addressing challenges around the world," according to a White House readout of the call.
"The two discussed opportunities to strengthen the partnership between the United States and India in broad areas such as the economy and defense," it disclosed.
On Twitter, PM Modi said he "had a warm conversation" with the new US president and that they had both "agreed to work closely in the coming days to further strengthen our bilateral ties". "Have also invited President Trump to visit India," PM Modi added after the White House revealed Washington had extended a similar invite for "later this year".
During his election campaign, Mr Trump courted Indian-American voters and his publicity material borrowed PM Modi's campaign catchphrase, tweaking it to say "Ab ki baar, Trump sarkaar."
A surprisingly warm conversation in November between then President-Elect Trump and Pakistan's Prime Minister Nawaz Sharif caused concern in India.
President Trump's chief strategist Steve Bannon described PM Modi's victory in the 2014 general election as the first phase in a "global revolt" against the existing order that culminated with the outcome of November's US polls.
While Mr Trump's decision this week to pull the United States out of a trade pact known as Trans-Pacific Partnership (TTP) caused some consternation in other Asian countries such as China and Japan, India was not part of the agreement. Analysts say that Mr Trump's proposed restriction on H1B visas allowing high-skilled foreign workers into the US could cause some friction with India.
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