The FBI issued an advisory - the second-highest alert condition that can be issued by the organisation - to members of InfraGard, a security information sharing programme based in the US.
Phyllis Schneck, co-chairman of the InfraGard National Executive Committee, said that while there had been no publicised evidence of cyberattacks, "increased vigilance would be appropriate for all information systems and services".
The advisory states: "The FBI has no information of any additional threats; however, infrastructure owners and operators should be at a heightened state of alert and should implement appropriate security measures."
The FBI is concerned that physical attacks on financial and military targets could be followed by co-ordinated cyberattacks against the nation's telecommunications grid.
There are also new fears that the attacks could produce increased numbers of attacks by US-based hackers against government and corporate sites in the Middle East. This, in turn, could lead to a corresponding increase in hacker attacks against US sites.
"Cyber-based actors are calling for cyberattacks against Arab nation/state networks and terrorist computer networks," said Ben Venzke, a terrorism expert and president of security analyst firm IntelCenter. "Expect Arab hackers to retaliate if attacks materialise."
Dain Gary, vice-president of Red Siren Technologies and a member of the InfraGard executive board, said his company has already shut down its Web site and limited remote access privileges to essential personnel.