"It's in nobody's interests that terrorists should be able to plot and communicate out of the reach of authorities," Andrew Parker, British intelligence chief said.
He said internet and telecom companies had an "ethical responsibility" to alert them of potential threats.
Asked if he supported increased surveillance powers, Parker said what should be included in new legislation was a matter "for parliament to decide".
"It is completely for ministers to propose, and Parliament to decide. It's a fundamental point about what MI5 is. It's for us to follow what's set by Parliament," he told BBC's Today programme in a first ever live interview.
MI5 is the United Kingdom's domestic counter-intelligence and security agency and is part of its intelligence machinery alongside the Secret Intelligence Service.
The current MI5 threat level from international terrorism for the UK is severe, meaning a terrorist attack is highly likely, Parker said.
This was partly the result of the rise of Islamic State, he said, but the shape of the threat had also changed because of the internet and social media, which was being exploited by ISIS.
"MI5 and others need to be able to navigate the internet to find terrorist communication, we need to be able to use data sets to be able to join the dots to be able to find and stop the terrorists who mean us harm before they are able to bring plots to fruition.
"We have been pretty successful at that in recent years but it is becoming more difficult to do it as technology changes faster and faster (and) encryption comes in," he added.
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