Prince Harry & Meghan Markle Wish Kate Middleton Well Amid Cancer Diagnosis

Prince Harry and Meghan Markle just wished Kate Middleton all the best amid her cancer diagnosis -- and they're especially hoping the public lets her deal with this in peace.

The Duke and Duchess of Sussex tell TMZ ... "We wish health and healing for Kate and the family, and hope they are able to do so privately and in peace."

As we reported ... Meg and Harry were out and about in L.A. Thursday night at an art exhibition -- and there was no indication that the Kate news was on their radar. Unclear if they were aware of her diagnosis or not, but in any case ... they're sending their love.

Of course, Harry jetted on over to London last month to see his father amid his own cancer diagnosis -- but again, we have no idea what King Charles knew about Kate's situation ... and what, if anything, may have been relayed to Harry at the time. His trip was very quick.

It goes without saying ... Harry and Will's relationship has been fractured in recent years -- especially after PH and MM left the Royal family to pursue their life here in California.

Still, this type of development trumps all that ... and that's reflected in H&M's statement.

Kate also asked for privacy during her announcement -- saying she and William are navigating this journey as delicately as they can ... especially with their children in mind.

The Princess of Wales did not disclose what type of cancer she's battling, but she says she's getting stronger each day -- which was evident in the video TMZ obtained of her out.