His remarks come just days before the government’s controversial Investigatory Powers Bill, also known as the Snoopers Charter, is due to be debated in the House of Commons.
Parker praised the work of his intelligence service, but said it would not be able to keep Britain safe unless it had permission to intercept communication data.
The director said Islamic State presents a “three dimensional” threat – at home, overseas and online – with more and more of MI5’s casework related to Syria and the extremist group.
“We are seeing plots against the UK directed by terrorists in Syria; enabled through contacts with terrorists in Syria; and inspired online by ISIL’s sophisticated exploitation of technology,” he said.
“It uses the full range of modern communications tools to spread its message of hate, and to inspire extremists, sometimes as young as their teens, to conduct attacks in whatever way they can.”
Speaking in London on Wednesday at a Lord Mayor’s event, Parker expressed his support for the new security bill, claiming any powers given to the security services must have “strict safeguards” in place.
“We do not seek sweeping new intrusive powers in that legislation, but rather a modern legal framework that reflects the way that technology has moved on, and that allows us to continue to keep the country safe,” he said of the bill.
Parker highlighted the importance of intercepting communication data, but added many forms of communication data are now unreachable be security services as apps and messaging services become more sophisticated.
“It may not yet have reached the high water mark, and despite the successes we have had, we can never be confident of stopping everything,” he said.
The spy chief added that current legislation would prompt debate.
“But I hope that the public debate will be a mature one, informed by the three independent reviews, and not characterized by ill-informed accusations of ‘mass surveillance’, or other such lazy two-worded tags.”
His speech follows direct pressure placed on tech and social network companies to continue monitoring communication data.
Parker told the BBC last month that tech companies had an “ethical” responsibility to hand over the data of any suspected terrorist.
“Those providers rightly want to maintain the privacy and security of their customers’ data – but they also have an obligation, and I would argue an ethical responsibility, to work with law enforcement and other agencies to prevent their services being used for the purposes of serious crime and terrorism,” he said.