Advances in technology are allowing terrorists to communicate "out of the reach of authorities", head of MI5 Andrew Parker has told the BBC.
The serving boss of the UK's home security agency told the Today programme it was becoming more difficult to obtain online information.
He said internet companies had an "ethical responsibility" to alert agencies to potential threats.
But MI5 was not about "browsing the lives" of the public, he added.
Ministers are preparing legislation on the powers for carrying out electronic surveillance.
Mr Parker, in the first live interview by a serving MI5 boss, said what should be included in new legislation was a matter "for Parliament to decide".
But Shami Chakrabarti, director of human rights group Liberty, said while she agreed that existing surveillance legislation was "inadequate", she was concerned about "any attempt to seek a blank cheque from the British public for unlimited surveillance".
by Gordon Corera, BBC security correspondent
A live interview by a serving head of MI5 is unprecedented. So why now?
The overall context is a terrorist threat, that MI5 says is growing, technological change and recent concerns over privacy and surveillance.
The government has made clear a new investigatory powers bill is expected soon and Andrew Parker and others are keen to make their case ahead of that.
Past attempts to increase powers were dubbed "the snoopers' charter" and failed, but the next bill is likely to differ - providing increased accountability and oversight.
The question of whether new legislation will maintain existing capabilities against a backdrop of technological change or provide new powers will not be clear until the detail is revealed.
But Andrew Parker's argument is that it's getting harder for his service to do its job.
One reason is that much of the communications material MI5 needs is held abroad, often by US companies, and he made clear he would like more co-operation from them.
There is recognition from the security and intelligence services that justifying their intrusive capabilities will require more transparency.
That openness may be provided not just by legislation but also by speaking publicly and even coming into a BBC studio.
Mr Parker said the shape of the terror threat had changed "because of the internet and the way terrorists use social media".
He said they were using secure and encrypted apps and the internet to "broadcast their message and incite terrorism among people who live here".
"Most of the people who try to become involved in terrorism in this country are born and brought up here, come through our education system", he said. But they had "decided the country of their birth is their enemy".
Media captionAndrew Parker said the threat was continuing to grow, largely because of the situation in Syria
He rejected the suggestion that MI5 tactics led to the radicalisation of targets and played down fears about extremists entering Europe among the thousands of refugees from Syria.
The MI5 chief also said there was a question of the ethical responsibility of companies like Facebook and Twitter to alert the authorities regarding information about terrorism, child sex exploitation and other criminal activity.
TechUK, the UK's technology trade association, said companies took their responsibility to support the work security services do "extremely seriously" but any obligations placed upon them "must be necessary and proportionate" and should be "based upon clear and transparent law agreed by Parliament".
'Close to critical'
It said the government needs to be clear about what is being asked of the industry on the issue of encryption and on the issue of reporting suspicious activity "the impact on the legitimate right for freedom of speech" must be safeguarded.