Foreign Minister Yashwant Sinha told the Indian parliament that al-Qaeda elements had taken shelter in Bangladesh.
"Though the foreign media has also reported several such instances, our own sources have also confirmed many of these reports," Mr Sinha said.
The comments come amid recent media reports and allegations by opposition parties in Dhaka that Bangladesh has become a safe haven for Islamist extremists.
No response
The Bangladesh Foreign Secretary Shamser Mobin Chowdhury refused to respond afresh to India's charges.
He said he would await a detailed text of Mr Sinha's parliamentary statement.
But two weeks ago, a Foreign Office spokesman in Dhaka strongly protested at similar remarks by the Indian Deputy Prime Minister, LK Advani, that Pakistani intelligence (ISI) and al-Qaeda had increased their activities since last general elections in Bangladesh.
The foreign secretary also summoned the Indian High Commissioner in Dhaka, Monilal Tripathi, and handed over a protest note, saying the allegations are baseless and incorrect, if not motivated.
Yashwant Sinha on Wednesday also accused Pakistan of misusing its high commission in Dhaka as a "nerve centre" for the activities of Pakistan's Inter-Services Intelligence agency.
He said a number of Islamic seminaries, or madrassas, had sprung up along the Bangladeshi border with India and that rebels fighting in India's north-east had established training camps in Bangladesh.
But he added that India had conveyed its "strong concern" to Bangaldesh and Dhaka in turn has given assurance it would not allow its territory to be used for anti-Indian activities.
"The Bangladesh Foreign Minister, intimated that instructions have been issued not to allow presence of Indian insurgents or their free movement across the border," Mr Sinha said.
The two neighbour have normally enjoyed friendly relations, but the issue of rebel bases in Dhaka has featured frequently over the past few months.