Proposed EU rules aimed at combating terrorist content could clash with an existing liability shield for websites and chill online expression, tech groups said.

The European Commission Sept. 12 proposed rules that would require Facebook Inc., Twitter Inc., and other tech companies to remove terrorist content within one hour of receiving notice from national authorities. The rules would also require companies to take proactive measures, such as using automated tools, to keep such content off their sites.

The EU’s proposal...