Karine Jean-Pierre kicked off her daily briefing Friday by acknowledging the White House heard the news out of Kensington Palace, and said their thoughts were with the Duchess of Cambridge, along with Prince William and the rest of the Royal Family

KJP wished Kate a full recovery, and then said she and the rest of the administration want to respect her privacy, and wouldn't comment further on the matter.

Jean-Pierre added that she wouldn't answer questions about whether the prez had spoken with any member of the Royal Family -- wisely anticipating what was coming next from the press corps -- and then moved on to other business.

It seems the news caught the White House about as off-guard as the rest of the world ... the Royal Family made no indication of Kate's health until she posted the video this morning at 11 AM PT telling the world about her diagnosis.

As we reported, Kate had abdominal surgery back in January, and she says tests run after the surgery showed cancer had been present. She started a round of preventative chemotherapy and only recently resurfaced in public.

President Biden has a close relationship with King Charles -- discussing climate change last summer on JB's first visit to the UK after Charles was crowned King, and First Lady Dr. Jill Biden actually met Kate while attending Charles' Coronation in May 2023.