Boris Johnson will be among EU foreign ministers meeting to consider measures to ensure there is "no safe space for terrorists" to plot attacks and share radical material online.
It comes in the wake of recent terrorist attacks in the UK and France.
The PM has urged Google, Facebook and Twitter to take down terrorist content.
It follows Theresa May's agreement of measures with G7 leaders in April and a new plan with French President Emmanuel Macron last week.
Speaking ahead of the meeting, Mr Johnson, the UK foreign secretary, said: "We are pushing back Daesh militarily, but the threat we face is evolving rather than disappearing as they lose ground in Iraq and Syria.
"The fight is moving from the battlefield to the internet.
"There should be absolutely no safe space for terrorists plotting attacks, radicalising young people and encouraging others to carry out violence in the name of an obscene ideology.
"We all want to protect our people so we must say together that enough is enough. Terrorism affects us all and we need a common approach to ensure the problem gets solved, and at a much faster pace than we are seeing right now."
Internet giants will face increased pressure to tackle online extremism as EU leaders are expected to back a drive for tougher web regulation.