Jaishankar's remarks came after he held talks with his Bangladeshi counterpart A K Abdul Momen here on issues like the long-pending pact on the Teesta water sharing and the Rohingya crisis.
Jaishankar is in Dhaka on a two-day visit, his first to Bangladesh after taking over the charge of External Affairs Minister.
Jaishankar said that he had a fruitful interaction with his Bangladeshi counterpart.
Jaishankar in a joint press conference with Momen said that the National Register of Citizens (NRC) in Assam is India's "internal matter" amid concerns in Bangladesh, Bdnews reported.
Home Minister Amit Shah early this month raised with Bangladesh India's concerns over the illegal immigration from Bangladesh to the Northeast. The issue was flagged before Bangladesh Home Minister Asaduzzaman Khan at the 7th meeting of India-Bangladesh Home Minister Level Talks (HMLT) held in New Delhi.
Jaishankar's remarks came ahead of the publication of the final list of the NRC in Assam on 31 August.
When the draft NRC was published last year, 40 lakh names were excluded, leading to a huge political controversy.
Assam and other Northeastern states have been facing the problem of influx from neighbouring Bangladesh through the porus border.
Jaishankar also said India’s position and commitment to the pending Teesta water deal remained as it was, Bdnews quoted Jaishankar as saying.
The Teesta deal was set to be signed during the then Prime Minister Manmohan Singh's visit to Bangladesh in September 2011, but was postponed at the last minute due to objections raised by West Bengal Chief Minister Mamata Banerjee.
Teesta water is crucial for Bangladesh, especially in the leanest period from December to March, when the water flow often temporarily comes down to less than 1,000 cusecs from 5,000 cusecs.
On water sharing, he said water resource is an “important subject" for Bangladesh and "we look forward to making progress to find a mutually acceptable formula from 54 shared rivers. We are ready to make a start wherever possible."
"We have a position you are aware of that. We have a commitment on that position and that does not change," he said when asked to comment specifically on the Teesta, indicating New Delhi’s previous position that it is ready to sign the deal once the West Bengal government agrees to it.
They also discussed the Rohingya issue and agreed on their “safe, speedy and sustainable return" to Myanmar.
Bangladesh, which is facing a big influx of Rohingya Muslims from Myanmar, is seeking enhanced India's support in handling the crisis by mounting pressure on Myanmar to take back the refugees who have taken shelter in the country.
According to the United Nations, over 745,000 Rohingya Muslims have fled Myanmar's Rakhine state into Bangladesh following serious human rights abuses.
However, Myanmar denies the allegations.
Jaishankar said connectivity between the countries has been increased on all routes and "we would like to step up this partnership".
On energy cooperation, he said both countries have stakes in each other’s success.
On trade, he said, the progress would be made at a pace which is comfortable for Bangladesh.
Jaishankar said India operates the largest consular service in Dhaka and “we want to make it seamless".
"Our partnership with Bangladesh remains an example what neighbours can do together," he said, adding that Prime Minister Narendra Modi is determined to ensure partnership remains a "role model" in South Asia.
Momen said he was "excited" as he had a "very good meeting" with Jaishankar.
"We more or less came to a consensus on all issues," he said, without naming the issues on the agenda.
Earlier, Jaishankar started his official engagements on Tuesday by paying respects to Bangladesh’s founding father Bangabandhu Sheikh Mujibur Rahman at the 'Bangabandhu Memorial Museum’ in Dhanmondi.