According to a report in New Scientist, FBI assistant director Shawn Henry said that as many as two dozen countries have taken an "aggressive interest" in penetrating the networks of US companies and government agencies.
US intelligence agencies have previously voiced concern that Russia and China have the ability to electronically spy on the US and disrupt computer networks.
Henry also said that organized crime groups are drawn by the ease of reaching millions of potential victims.
Cyber attacks are climbing the list of worries for foreign policy officials all over the globe.
In August, Georgia accused Moscow of conducting "cyber warfare" against its government sites, at the same time as Russian troops began a conventional attack.
US federal agents are working with foreign counterparts where the rising wave of computer attacks has awakened international interest, according to Henry.
NATO established a "cyber defence" centre in Estonia earlier this year, a country brought to its knees by internet-based attacks in 2007.
"Over the past year, the malicious activity has become much more prevalent," Henry said. "The threat continues to increase," he added.
Earlier this year, an Organisation for Economic Co-operation and Development report said that international cooperation must be stepped up to head off the economic and security consequences of cyber crime.
According to Henry, Botnets, networks of computers controlled remotely by hackers without their owners realising, are growing in popularity with criminals. They can be used to bring down systems connected to the internet, or to steal information.
Around one in four US personal computers are part of a botnet.
"Spearfishing," when hackers get a copy of a company's email list, then send out official-looking requests for employee personal information, has also been a growing problem.
Henry said that computer crime has even invaded Wall Street.
Some investment companies have lost tens of millions of dollars through "pump and dump" schemes in which criminals achieved control of multiple client accounts.
The accounts are used in concert to run up the price of low-liquidity stocks. Others then make a large profit when they sell, "dump" shares bought at the earlier, low price.