Amber Heard has broken her silence on her split from boyfriend Elon Musk, saying they still "care deeply for one another" and "remain close".

The Justice League actress and the tech billionaire had been dating for more than a year, according to US showbiz publication People, and this week rumours began swirling that they had parted ways.

Heard decided to address the media speculation in an Instagram post, sharing a series of photos with the words "Give", "Love" and "Joy" spelled out with rose petals, along with the caption: "Being in the public eye means having to explain yourself to so many people, so much of the time.

"In this case, I'd like to remain more quiet. Although we have broken up, Elon and I care deeply for one another and remain close. Thank you for the continued support, respect, and privacy during these difficult, very human times."

Forty-six-year-old Musk referenced the break-up in the comments section of Heard's previous Instagram post, which showed her comparing herself to The Little Mermaid's Ariel.

He said the photo was "V cute", before adding: "Btw, just to clear up some of the press storm this weekend, although Amber and I did break up, we are still friends, remain close and love one another. Long distance relationships when both partners have intense work obligations are always difficult, but who knows what the future holds."

Heard and Musk were first romantically linked last year when they were spotted out together several times during their respective divorces from actors Johnny Depp and Talulah Riley.

Thirty-one-year-old actress Heard filed for divorce from Depp after 15 months of marriage in May 2016, and days later filed a domestic violence restraining order against him. The couple reached a divorce settlement three months later.

Tesla CEO Musk has five sons with his first wife Justine Musk, and then went on to marry and divorce his second wife, actress Talulah Riley, twice.