Friends of Michael Douglas and Catherine Zeta-Jones hope the Hollywood stars can still save their marriage.
The couple have temporarily separated, with a spokesman for Zeta-Jones saying they are "taking some time apart to evaluate and work on their marriage".
Douglas' publicist, Allen Burry, echoed Zeta-Jones' statement and declined to comment further.
The star of Wall Street and the Welsh-born actress have suffered a number of setbacks in recent years. Douglas, 68, was diagnosed with throat cancer in 2010, and Zeta-Jones, 43, has revealed that she suffers from bipolar II disorder.
The couple have not been photographed publicly together since a gala event in Manhattan in April, which had led to rumours of a split. Last week Douglas was seen playing golf in Sardinia while his wife stayed at home in New York with their two children, son Dylan, 12, and 10-year-old daughter Carys.
This week Douglas dined with friends at a restaurant in Nice.
He is due to attend the Deauville American Film Festival in France this week, the same festival where he was introduced to Zeta-Jones by his friend the actor Danny DeVito in 1998.
They made the decision to separate around the time Douglas said his throat cancer had been caused by oral sex.
Those close to the couple said neither had filed for divorce, nor moved towards a legal separation. One said: "They want the best for their kids, no matter what happens."
Douglas and Zeta-Jones married in New York in 2000 and they are thought to have signed a pre-nuptial agreement that would entitle Zeta-Jones to millions of dollars in a divorce.
When Douglas divorced his wife Diandra after two decades in 2000, he handed over about $58 million, one of Hollywood's biggest settlements.
Douglas and Zeta-Jones decided to take time apart soon after he returned home in May from the Cannes film festival - where he was promoting Behind the Candelabra in which he stars as Liberace - according to People magazine.
During an interview in Cannes, which was published in early June, Douglas said his throat cancer, from which he is now in remission, had been caused by oral sex.
He described contracting HPV, a sexually transmitted virus which is a common cause of cervical cancer, but can also cause throat cancer. A publicist for the actor later suggested he was not talking about his own cancer.
A few days later television host and friend of the pair Barbara Walters told millions of viewers that the virus "did not come from Catherine".
She said: "Michael would like everyone to know that his wife, Catherine, is healthy. She does not have the HPV virus. He doesn't know how he got cancer. He does not want anyone to think it was from Catherine."
In an interview last month, Zeta-Jones described dealing with her husband's cancer, saying: "Together we all coped with everything. It did make us closer. But I wouldn't wish it on anybody."
She was first admitted to a rehabilitation clinic in the US in 2011 and doctors concluded she suffered from bipolar II disorder, which is characterised by extreme mood swings.
Zeta-Jones has spoken candidly about her battle with the disorder. She admitted herself to hospital for "maintenance" treatment in April.
Zeta-Jones began her career as a stage actor before gaining fame in Britain on ITV's The Darling Buds of May and moving to Hollywood. She won the best supporting actress Oscar for her performance in 2002's Chicago.
Douglas is the son of Hollywood star Kirk and has won two Oscars.
• Michael Douglas and Catherine Zeta-Jones married in 2000.
• They have two children: Dylan, 12, and Carys, 10.
• Zeta-Jones, at 43, is 25 years younger.
• Asked before the split what kept them together, Zeta-Jones said: "Respect, space and a sense of humour."