He also warned businesses that they had a responsibility to stop their systems from being hijacked for denial of service attacks.
Alexander told delegates to the Information Security Solutions Europe conference of the significance of a new approach to electronic security in the aftermath of the US terrorist attacks.
"The terrorist attack on America has put a new and intense focus on information security," said Alexander. "Tony Blair's fight against terrorism will exist on many levels and IT security will be a major part of it. This is crucial for a safer society and a safer economy."
The e-minister warned that there must be a collective responsibility for security and that businesses used by hackers to attack other businesses must take a share of the blame.
"Businesses that have gaps in their security and, for example, act as a platform for denial of service attacks must be held responsible for their role in the attack," he said.
Alexander warned that businesses would be expected to get their security in order, and that the government would do the same with its e-government projects.
He highlighted the national Information Security Standard BS7799 as a key part of developing best practice for trading online. He also singled out the tScheme, a voluntary accreditation scheme for Trusted Service Providers, as an imaginative self-regulatory response.
Alexander added that the government would work hard to address consumer concerns over online transactions by promoting a code of practice and guidelines that will speak directly to users.