Writing in the Financial Times, Robert Hannigan says some US tech companies are "in denial" about how their services are being misused.
He also said UK security agencies needed support from "the largest US tech companies which dominate the web".
Extremist groups in Syria and Iraq had "embraced the web", he added.
Mr Hannigan argues that the big internet firms must work more closely with the intelligence services, warning that "privacy has never been an absolute right".
"However much they may dislike it, [US technology companies] have become the command and control networks of choice for terrorists and criminals, who find their services as transformational as the rest of us," he writes.
"The challenge to governments and their intelligence agencies is huge - and it can only be met with greater co-operation from technology companies.
"GCHQ and its sister agencies, MI5 and the Secret Intelligence Service, cannot tackle these challenges at scale without greater support from the private sector, including the largest US technology companies which dominate the web."
The debate about whether security agencies should be allowed to access personal data through social-networking sites like Google and Facebook was brought to the fore in 2013 after Edward Snowden leaked details of alleged internet and phone surveillance by US intelligence.
Mr Snowden, who has been granted temporary asylum in Russia, faces espionage charges over his actions.Analysis
Gordon Corera, BBC security correspondent
This is a hard-hitting article from the new GCHQ director in his first move on taking up the role. His aim is clear - to pressure tech companies to work more with government.
Following the Edward Snowden disclosures last year, some of those companies have been less willing to share data with intelligence and law enforcement and more inclined to encrypt it - making it harder for authorities to gain access.
Tech companies may be surprised by the ferocity of the attack. And they - and privacy activists - may also argue that the spies started this fight with the scale of their intelligence collection and by hacking into some of those companies.
But Robert Hannigan has wasted no time in wading into the debate over security and privacy and making clear he will not shy away from a fight.
Mr Hannigan goes on to say that Islamic State (IS), also known as Isil, has a different approach to using the internet than other extremist groups have had.
"Where al-Qaeda and its affiliates saw the internet as a place to disseminate material anonymously or meet in 'dark spaces', Isis has embraced the web as a noisy channel in which to promote itself, intimidate people, and radicalise new recruits."
He also says most internet users "would be comfortable with a better and more sustainable relationship between the [intelligence] agencies and the tech companies".
Brent Hoberman, founder of lastminute.com, said he thought there should be a compromise.
He said: "We need more trust in the security services, I agree, and there were too many people that had access to Snowden files - 800,000 people or something - that's too many for high level security.Mr Hannigan was appointed as the new director of GCHQ in April
"But if we had enough confidence that they were only under due process with a warrant that was specific in limited cases - I want the security services to be able to get into my phone."
Rachel O'Connell, a former chief security officer at social networking site Bebo, said the security services were taking a "polarised position".
She said this was the case "particularly post-Snowden, where we were realising that there was a suspicion, in some cases substantiated, that the security services have total access to whatever is happening online.
"And that's a situation that's untenable if you are thinking about a democracy."Hashtags strategy
Earlier in the year an investigation by the Guardian revealed how IS was using popular hashtags - including ones used during the Scottish Referendum - to boost the popularity of its material on Twitter.
Security minister James Brokenshire met recently with representatives from technology companies - including Google, Microsoft and Facebook - in Luxembourg to discuss ways to tackle online extremism.
The government's Counter Terrorism Internet Referral Unit (CTIRU), set up in 2010, has removed more than 49,000 pieces of content that "encourages or glorifies acts of terrorism" - 30,000 of which have been removed since December 2013.
Scotland Yard's head of counter-terrorism, Assistant Commissioner Mark Rowley, has previously said that officers are removing more than 1,000 online postings a week, including graphic and violent videos and images.