The prime minister, Anthony Albanese, says Australians are “sending support and strength” to the Princess of Wales after her announcement she is receiving chemotherapy to treat cancer.

“My thoughts, and those of Australians, are with the Princess of Wales and her family following the news of her cancer diagnosis,” he posted on X on Saturday.

Albanese said Catherine showed “extraordinary courage” with her public statement.

“We are sending support and strength in this difficult time as she undergoes treatment, and we wish her well for a speedy recovery.”

The former prime minister Scott Morrison also wished the royal family well.

“Sending love and praying for a full recovery of Princess Catherine as well as comfort and support for Prince William, Prince George, Princess Charlotte and Prince Louis,” he posted on X.

The Australian Monarchist League invited its members and supporters to sign a card for Catherine sending wishes “for a speedy recovery and for strength and perseverance”.

“Our hearts go out to The Princess of Wales on hearing the news that she is undergoing chemotherapy treatment for cancer,” the league said.

“Our thoughts and prayers are also with the Prince of Wales and the children at this time.”

Catherine revealed the news in a video message at 6pm local time (5am AEDT), saying the diagnosis was a “huge shock”.

The 42-year-old said she was told she had cancer after undergoing abdominal surgery nine weeks ago at the private London Clinic.

“The surgery was successful,” she said in the video message. “However, tests after the operation found cancer had been present.

“My medical team therefore advised that I should undergo a course of preventive chemotherapy and I am now in the early stages of that treatment.”

The news comes after weeks of speculation about the royal’s health.

“This of course came as a huge shock, and William and I have been doing everything we can to process and manage this privately for the sake of our young family,” Catherine said in the video message.

“As you can imagine, this has taken time. It has taken me time to recover from major surgery in order to start my treatment.

“But, most importantly, it has taken us time to explain everything to George, Charlotte and Louis in a way that is appropriate for them, and to reassure them that I am going to be OK.”

King Charles praised his daughter-in-law’s courage and said the two remained close, in a statement issued shortly after the announcement.