ASIO will be given powers to spy on Australians who are working on behalf of a foreign power, under a comprehensive rewriting of intelligence laws that also overhauls how agencies can intercept telecommunications.

Attorney-General Christian Porter said former senior mandarin Dennis Richardson had identified a "gap" in ASIO's surveillance powers. At present ASIO can spy on Australians when they pose a threat to security or engage in foreign interference or espionage activities.