His remarks came while speaking to the media on Sunday after launching the 'Corruption Prevention Week 2017' at the graft watchdog's headquarters in Dhaka.
"Police have busted several militant hideouts recently and found huge amount of cash. These funds came through the banking system. It did not come out of thin air," said ACC Chairman Mahmood.
He said the ACC has asked banks to comply with regulations for transactions, which will automatically stop terror-financing.
"Funds for terrorists come through banking channels and through informal channels, which I reckon is not that much."
He said the National Board of Revenue (NBR), Bangladesh Bank and the ACC were working in tandem to stop informal money transaction channels.
"Now the banks are strict on disbursing loans and financial transactions. I believe a proper banking system can stop terror financing."