The Unfaithful star cancelled a flight back to Los Angeles, where he was due to start shooting The Snow Goose, to be by his famous girlfriend's side in her time of need.
Martinez contacted his agent to inform him he would be staying in Australia with Minogue, who was diagnosed with the disease earlier this week.
The actor's dad Robert says, "Olivier just wants to be with Kylie. That's all that's important to him now."
Martinez was reportedly the one who encouraged Minogue to visit a doctor following prolonged bouts of tiredness.
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