After meeting Hasina, he expressed confidence that bilateral ties will be taken to a new level.
"Delighted to welcome H.E. Sheikh Hasina, the Prime Minister of Bangladesh, on her State Visit to India," he tweeted later.
"PM Sheikh Hasina and I are determined to take the relationship between our nations to a new level," he added in another tweet.
Hasina arrived here on a four-day visit, which comes after a gap of seven years.
Newsagency PTI says she will hold wide-ranging talks with Modi on Saturday during which India is also set to announce a line of credit of USD 500 million to Bangladesh for military supplies.