PARIS—Security-chip maker Gemalto NV said Wednesday that American and British intelligence services could be responsible for a “particularly sophisticated intrusion” of its networks several years ago, but denied that the alleged hack could have widely compromised encryption it builds into chips used in billions of cellphones world-wide.

The company, one of the world’s largest makers of cellphone SIM cards, on Wednesday disclosed the first details of an internal investigation it launched in response to a report Friday that...