LONDON — One of Britain’s highest-ranking intelligence officials on Tuesday castigated the giant American companies that dominate the Internet for providing the “command-and-control networks of choice for terrorists and criminals” and challenged the companies to find a better balance between privacy and security.

The statements were made by Robert Hannigan, the newly appointed director of GCHQ, Britain’s electronic intelligence agency. They were among the most pointed in a campaign by intelligence services in Britain and the United States against pressure to rein in their digital surveillance after disclosures by the American former contractor Edward J. Snowden.

Mr. Hannigan’s statements were among the most critical of American technology firms by the head of a major intelligence agency; the accusation went beyond what United States officials have said about Apple, Google and others that are now moving toward sophisticated encryption of more and more data on phones and email systems.

But the companies, saying they are responding to demand from their users, show no signs of backing down. Recently the chief executive of Apple, Tim Cook, said governments that want data should deal with the users of the technology, not with the providers of the hardware and services. Brad Smith, the general counsel of Microsoft Corporation, told a Harvard Law School symposium on Tuesday that, if anything, companies like his “will move to strengthen encryption,” and require governments to get court orders if they want data.