When President Obama and Prime Minister Narendra Modi of India hugged and said their goodbyes in January after Mr. Obama’s state visit to India, the two leaders promised to keep in touch.

Mr. Modi had said that he and Mr. Obama “talk with ease on the phone,” and the chemistry between them was indicative of the growing closeness between their countries.

“We have decided to give this critical partnership a new thrust and sustained attention,” Mr. Modi said at the time.

Since world leaders are not inclined to maintain a friendship on Facebook or conduct top-level diplomatic communications via WhatsApp, the two countries established a hotline between Washington and New Delhi that just recently became operational, senior White House officials said this week.