A spokesman in Dhaka described claims by Indian Foreign Minister Yashwant Sinha on Wednesday that al-Qaeda elements were in Bangladesh as "baseless and unfortunate".
Such comments by the Indian leadership went against the "spirit of good neighbourliness", Foreign Secretary Shamser Mobin Chowdhury said.
At the same time, Pakistan has dismissed suggestions by India that Pakistani intelligence is using the high commission in Dhaka to co-ordinate anti-Indian activity.
Bangladesh has also said it was not aware of such activities by the Pakistani mission.
"Any such charge has to be backed by credible evidence," Mr Mobin said.
The spat comes amid recent media reports and allegations by the opposition in Bangladesh that the country has become a safe haven for Islamist extremists.
Rebels
In a statement, the Pakistani Foreign Ministry described the Indian allegations as "malicious and preposterous".
It said the high commission in Dhaka was "working within internationally accepted norms".
Mr Sinha told parliament on Wednesday that Pakistan was using its high commission in Dhaka as a "nerve centre" for the activities of its Inter-Services Intelligence (ISI) agency.
He also 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.
He said India had conveyed its "strong concern" to Bangladesh and Dhaka in turn had 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 neighbours have normally had friendly relations, but the issue of rebel bases in Dhaka has featured frequently over the past few months.
Two weeks ago, the Foreign Office in Dhaka protested when Indian Deputy Prime Minister LK Advani said the ISI and al-Qaeda had increased their activities since general elections a year ago in Bangladesh.