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".
Meanwhile, a highly critical report from David Anderson QC, the independent reviewer of terrorism legislation, warns forthcoming separate legislation to ban extremism could provoke a damaging backlash in Muslim communities.
The lawyer said in his annual report that if the new laws were too widely drawn, they could play into the hands of people trying to encourage extremism and terrorism.
MI5 boss Mr Parker also told the BBC:
- The terrorism threat is the "most serious threat Britain faces in security terms"
- Six alleged terror plots have been foiled in the past 12 months, which Mr Parker said was the highest number he could recall in his 32-year career "certainly the highest number since 9/11"
- MI5 had to "make choices" about where to put resources, and make sure they were "focused where the sharpest threat is"
- On the killers of Fusilier Lee Rigby: "There cannot be a guarantee that we will find and stop everything. That's not possible. We can't monitor them all the time."
- He rejected the suggestion that security service tactics can lead to radicalisation saying it was "completely untrue"
- He paid tribute to the people who work at MI5 and their work "which so often goes unrecognised"
He said online data encryption was creating a situation where the police and intelligence agencies "can no longer obtain under proper legal warrant the communication of people they believe to be terrorists".
It was a "very serious" issue, he said, adding: "It's in nobody's interests that terrorists should be able to plot and communicate out of the reach of authorities."
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".
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.
The UK's terror threat is rated as "severe", which means an attack is highly likely.
BBC security correspondent Frank Gardner said the UK was "pretty close to the cusp" of the highest terror threat rating of "critical", which means an attack is expected imminently.
Profile: Andrew Parker
- Became head of MI5 in April 2013, succeeding Sir Jonathan Evans
- He had been deputy director general of the security service since April 2007
- He has more than 30 years professional experience in national security and intelligence work, including in the fields of international terrorism, serious and organised crime and counter-espionage
- In 2005 he led MI5's response to the terrorist attacks in London
- Holds a degree in natural sciences from Cambridge University
- He is married with two children
- The MI5 website describes him as a keen ornithologist and wildlife photographer