The security minister, Ben Wallace, has said that a Conservative government would increase the pressure on social media companies to help fight online extremism in the wake of the Manchester Arena attack.

He said ministers were open to consider financial penalties or a change in the law in order to encourage more action from technology companies – giving one example of guidance from Facebook that he said was “totally unacceptable”.

Wallace stressed that the technology firms had shareholders who were interested in the way they behaved. “For example, a number of these companies make money using algorithms … that encourage you to keep watching content that perhaps is not healthy for you to watch, and they set that up to maximise their profits,” he told Pienaar’s Politics on BBC Radio 4.

He said there were firms that were highly engaged on the issue but said others needed to do much more. “Let me give you an example,” he said. “The Facebook guidance to its moderators says it is OK to publish abuse of under-seven-year-old children from bullying as long as it doesn’t have captions alongside that. That is totally unacceptable and it doesn’t have to take an individual to do that. There are lots of ways you can moderate that automatically.”

The comments came after a Guardian investigation – the Facebook Files – exposed serious weaknesses in the way the company moderates content.

Theresa May placed the issue at the heart of her first G7 meeting in Sicily, persuading world leaders to back her calls for an international drive to persuade companies to take more steps to suppress extremist content online.

She suggested that the fight against Islamic State was shifting from the “battlefield to the internet”, in a move that won the backing of the US president, Donald Trump.