- Video report by ITV News Correspondent Geraint Vincent
The Home Secretary has urged tech companies to stop providing "a secret place for terrorists to communicate with each other".
Amber Rudd supports encrypted messaging services like WhatsApp - but says intelligence agencies should be allowed to read suspected terrorists' messages during investigations.
It comes after reports that Westminster terrorist Khalid Masood used WhatsApp seconds before launching Wednesday's attack, but agencies are unable to see what was communicated.
On encrypted messaging services, Ms Rudd told BBC One's Andrew Marr Show: "It is completely unacceptable, there should be no place for terrorists to hide."
Her stance has been criticised by technology experts who said there were serious legal, ethical and practical obstacles to offering security agencies a "back door" to view encrypted messages.
In an interview today, the Home Secretary left the door open to changing the law if necessary.
But she said she would rather see an industry-wide board doing it independently, as the best people to take action are those who understand the technology and the "necessary hashtags".
Ms Rudd also insisted the likes of Google, which runs the social video sharing platform YouTube, and smaller sites such as WordPress must realise that they are now acting as publishers and should take more responsibility for taking down extreme material.
"We need to make sure that organisations like WhatsApp, and there are plenty of others like that, don't provide a secret place for terrorists to communicate with each other," she said.
However, experts have said there could be serious practical obstacles to forcing companies to open up encrypted messages to security services - and also ethical questions over whether it was proportionate.
James Temperton, senior editor at Wired, told ITV News that any such move to offer a "back door" for security services would mean every single message sent through the platform would no longer be secure.
Mr Temperton said that any move to force tech companies to reveal encrypted messages would require a change in law - and those wishing to hide their messages might then move to other services based elsewhere and thus not subject to UK legislation.
Ms Rudd spoke out on the issue on Sunday morning after internet and social media companies came under fire over their failure to remove extremist material from the web.
In an interview in the Sunday Times, Foreign Secretary Boris Johnson attacked internet giants, accusing them of "not acting when they are tipped off", while Home Secretary Amber Rudd, writing in the Sunday Telegraph, said companies needed to be more "proactive".
Mr Johnson accused internet companies of a "disgusting" failure and called on companies like Facebook and Twitter to develop new technology to detect and remove jihadist and other extreme material.
"I'm furious about it. It's disgusting," he said. "They need to stop just making money out of prurient violent material."
Jihadist material is accessible in cyberspace. In the days ahead of the Westminster attack, internet giant Google had already been forced to promise it would take a "tougher stance" on hateful online content.
That followed the recent outcry and boycotts from advertisers after it became apparent their content was appearing alongside extreme material.
Mr Johnson said online media companies were "not acting when they are tipped off".
"Evil flourishes when good men do nothing - and that's what's happening here. They are putting up adverts next to it," he said.
A spokesman for WhatsApp stressed that they were cooperating with police.
“We are horrified at the attack carried out in London earlier this week and are cooperating with law enforcement as they continue their investigations, they said.