Christopher Wray said the US security services and MI5 are seeing more attacks carried out with crude weapons and little planning or training.
At the end of joint meetings with MI5, Mr Wray said it was vital for security services to share intelligence quickly.
MI5 head Ken McCallum said they faced a "very difficult cocktail of risks".
The FBI director said there are "very few dots out there", referring to intelligence on planned attacks, adding there was less time to connect those dots.
Working with MI5 in some cases was vital, he explained..
"If we're not super lashed-up, we're going to miss the only picture that's out there - and it's got to happen really fast," he said.
He said travel and technology had "blurred the lines between foreign and domestic threats" and that the encryption provided by technology companies was providing "an entirely unfettered space" for criminals and terrorists to operate.
Mr McCallum said around one in five terrorism investigations in Great Britain were linked to neo-Nazi, racist ideology or other related extremism - a rate that had remained roughly steady.
He said MI5 continued to see a growing role for juveniles and an obsessive interest in weaponry.
The two men said that co-operation allowed their agencies to cover a broader range of threats.
The FBI director said he had met British intelligence and security officials during his visit this week, which came as he marked 80 years of formal co-operation between the FBI and the UK.
On Friday afternoon his visit included looking at case studies of Russian and Chinese intelligence operatives moving around the globe.
Mr McCallum said the expulsion of Russian diplomats after the Salisbury poisonings in 2018 and continued refusal of visas had prevented Moscow rebuilding its presence and had constrained the threat in the UK.
Cyber threats had also been high on the agenda for discussions, Mr Wray said.
On Wednesday, the two security chiefs made an unprecedented joint public appearance to warn of an "immense" threat from China.
They spoke to business and academic leaders inside MI5 headquarters at Thames House in central London.