Major-General Jahangir Alam Chowdhury, head of Bangladesh's border guards, on a visit to India for regular border talks, said on Friday the suspected culprits had links with Bangladesh's giant neighbour.
He told a news conference in the Indian capital that security forces have traced the route of the attackers and the explosives used to a neighbouring country.
Asked which neighbouring country he was referring to, he said: "It is you, it is you I am telling, India."
Chowdhury suggested that criminals from both Bangladesh and India may have conspired with the militants to carry out the attacks.
India swiftly denied the charge.
"The government of India is deeply shocked and dismayed at the remarks ... alleging that some persons had gone across from India and were involved in the serial bomb blasts," the Indian foreign ministry said in a statement.
"This is a baseless and scurrilous allegation and is all the more shocking because it has been made against a friendly country," the statement said.
About 100 people were also wounded when some 500 small bombs went off on 17 August outside key buildings across Bangladesh in just half an hour.
"This is a baseless and scurrilous allegation and is all the more shocking because it has been made against a friendly country"
Indian foreign ministry
The outlawed Islamist Jamaat-ul-Mujahideen, or the Party of Holy Warriors, left leaflets at the sites demanding democracy be abandoned and an Islamic state established under sharia law.
Normally friendly relations between India and Bangladesh have been marred in recent years by border skirmishes and charges by the neighbours that the other harbours insurgents.
India also blames Bangladesh for the illegal migration of tens of thousands of poor Bangladeshis who cross the porous border in search of a livelihood. Dhaka denies the charge.
New Delhi has offered Dhaka help to hunt the perpetrators of the bombings.
About 400 suspected militants have been arrested so far in connection with the attacks.