Prince Charles has reached out to his supporters following his coronavirus diagnosis.

In a tweet shared on Thursday, Clarence House thanked everyone on behalf of the Prince of Wales for their "Get Well Soon" messages, and said he was "enormously touched" by the public's response.

On Wednesday, Clarence House announced Charles has tested positive for the coronavirus, explaining that the 71-year-old was displaying mild symptoms, but was otherwise in "good health".

The Duchess of Cornwall, 72, has also been tested but does not have the virus.

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"In accordance with government and medical advice, the Prince and the Duchess are now self-isolating at home in Scotland," a statement said, referring to the royal family's Balmoral estate.

"The tests were carried out by the NHS [National Health Service] in Aberdeenshire, where they met the criteria required for testing.

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"It is not possible to ascertain from whom the Prince caught the virus owing to the high number of engagements he carried out in his public role during recent weeks."

The Prince's last public engagement was on March 12, when he attended a dinner at Mansion House hosted by the Lord Mayor of London and the High Commissioner for Australia, George Brandis.

The dinner was in aid of the Australian bushfire relief efforts.

The Prince also had a number of private meetings with Highgrove and Duchy individuals, all of whom have been made aware.

He also reportedly attended an event with Prince Albert of Monaco on March 10, who later tested positive for the virus on March 19.

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Charles' doctor estimates the royal was contagious from March 13, a source said.

Buckingham Palace said the Queen last saw Charles two weeks ago.

"Her Majesty the Queen remains in good health," it said.

"The Queen last saw the Prince of Wales briefly on March 12 and is following all the appropriate advice with regard to her welfare. We will not be commenting further."

A small number of people living and working at Birkhall – the Prince's retreat on the Balmoral estate – are still at the residence and are now self-isolating.

The source said the Prince and the Duchess were in good spirits and the Prince was up and about and not bedridden.

Medical advice is that it's unlikely to escalate into a more serious case.

Covid19.govt.nz: The Government's official Covid-19 advisory website