Pop star Mariah Carey and her fiance, casino and resort mogul and Hollywood producer James Packer, have been apart for a month following an argument in Greece, and their relationship appears to be fracturing.

“They are trying to work it out,” Carey’s representative told “Entertainment Tonight” on Thursday. “Right now, they’re not sure if they will stay together. They are discussing it, and plan to release an official statement together about their future.”

The rep dismissed a report Wednesday by the Australian magazine Woman’s Day that said the Huntington-born and Greenlawn-raised Carey, 47, and Packer, 49, had ended their relationship over her allegedly extravagant spending habits. It also did not involve any inappropriate action on her part with a dancer from her Las Vegas residency, the representative added, saying, “The fight was not because of any cheating allegations or excessive spending by Mariah.”

The spokesperson did not address claims that issues regarding Carey’s upcoming E! reality show “Mariah’s World” were to blame for the breakup.

TMZ.com Thursday noted that Carey’s former husband, singer-actor and “America’s Got Talent” host Nick Cannon, with whom she has 5-year-old twins Moroccan and Monroe, attended her Halloween party over the weekend though Packer did not.

Carey and Packer, who began dating last year, became engaged on Jan. 21 in New York. Besides Cannon, her second husband, Carey previously was wed to music producer Tommy Mottola. Cannon and Carey separated in 2014.

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Packer, the son and grandson of Australian media barons, heads the gaming and resort conglomerate Crown Ltd. and owns the Hollywood production company RatPac Entertainment with filmmaker Brett Ratner. His marriage to swimsuit model Jodhi Meares, which ended in 2002, produced no children. In September 2013, Packer and his second wife, former model Erica Baxter, announced they were separating after six years of marriage. The couple has three children.