The company said it had a "temporary network issue" which affected calls and texts during Saturday afternoon and evening.
It said calls had since been restored and that it is working to restore full service.
But some users on Twitter complained of their texts being sent to random numbers instead of their contacts.
A spokeswoman said the company was "currently investigating the cause of the service disruption" and that it apologised for any inconvenience.
It also said that some "customers and non-customers" may have received a message from an unknown sender on Saturday.
In a statement on its website, the company said its advice "is to ignore all text messages that you deem incorrect".
Three, which has about nine million customers, experienced a data breach last year which saw personal details, including names and addresses, accessed unlawfully.
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Mobile phone company Three has apologised after some of its customers were unable to make calls or texts.