The Australian Federal Police have announced they are investigating thousands of unsolicited text messages designed to scare voters about Medicare on election day.

Voters received a message from ‘Medicare’ which said that prime minister Malcolm Turnbull was planning to privatise the service.

They read: “Mr Turnbull’s plans to privatise Medicare will take us down the road of no return. Time is running out to save Medicare.”

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The messages infuriated Mr Turnbull, while the Department of Human Services said they were not involved.

A News Corp report claims that the Queensland Labor branch say they sent the texts.

“The Australian Federal Police can confirm it received a referral on Saturday in relation to the receipt of text messages allegedly sent from Medicare,” a police spokesman said.

“This matter is now being evaluated and whilst this occurs it would not be appropriate to further comment.”

Mr Turnbull addressed the issue in his speech early on Sunday morning (AEST).

“Even as voters went to the polls … there were text messages being sent to thousands of people across Australia saying that Medicare was about to be privatised by the Liberal Party,” he said.

“The SMS message … said it came from Medicare. [It is] an extraordinary act of dishonesty.”