"Glad to receive ... John Sullivan. Discussing the deep convergences of our strategic relationship," Jaishankar tweeted with a picture of the two sides seated for talks.
The talks come as the US reaffirmed that there was no change in its Kashmir policy.
The US team led by Sullivan is in Delhi after a visit to Bhutan where the US official held talks with King Jigme Khesar Namgyel Wangchuck, Prime Minister Lotay Tshering and other officials.
In Bhutan, where China is attempting to slowly expand its reach, Sullivan discussed a range of issues, including the importance of protecting and enhancing a rules-based order in the Indo-Pacific region.
He also discussed the importance of expanding the two nations' people-to-people ties and joint efforts to combat trafficking in persons.
In a meeting with the Loden Foundation, the Deputy Secretary learned about efforts to promote entrepreneurship and cultural preservation in Bhutan.
He also affirmed the US support for science, technology, engineering and math activities that aim to benefit Bhutanese students, teachers, engineers, scientists and entrepreneurs, said US spokesperson Morgan Ortagus.
On Thursday, US Secretary of State Mike Pompeo, greeted the people of India on the 73rd Independence Day.
In a message, he said: "The US and India have enjoyed close ties of friendship since the US supported India's independence 72 years ago. Our shared democratic values, strong people-to-people ties and commitment to economic growth further cemented our relationship.
"Over the past two decades, our friendship has flourished into a strategic partnership, and we now cooperate on a range of important issues, from defence and counterterrorism, to freedom of navigation and cutting-edge science, including in space.
"As I said during my recent visit to India, the United States and India are great democracies, global powers and good friends. I wish the people of India a joyful Independence Day," Pompeo said.
( With inputs from IANS )