The influence of the network – damaged by US efforts to choke funding – is waning, the official said.
The Taliban, meanwhile, are in better financial shape, bolstered by Afghanistan‘s booming trade in drugs.
According to Mr Cohen, the al-Qaeda leadership has already warned that a lack of funds was hurting the group’s recruitment and training efforts.
“We assess that al-Qaeda is in its weakest financial condition in several years and that, as a result, its influence is waning,” Mr Cohen said from Washington.
But he added that as the organisation had multiple donors who were “ready, willing and able to contribute” the situation could be rapidly reversed.
However, the assistant secretary for terrorist financing said that the Taliban were in a better financial position, despite efforts to control the movement’s cash supply.
The many sources of funding for the Taliban make it more difficult to intercept and interrupt money flows, Mr Cohen said.
He also noted a trend in militant organisations turning to criminal activities to finance themselves.
Hezbollah, he alleged, is involved in making and selling illegal copies of music and computer software, as well as cigarette smuggling.