The Rolling Stones have have called off tour dates in Australia and New Zealand following the death of fashion designer L'Wren Scott, Mick Jagger's longtime girlfriend.

The iconic band said in a statement Tuesday they "are deeply sorry and disappointed to announce the postponement of the rest of their 14 ON FIRE tour."

Band members thanked fans "for their support at this difficult time."

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The Stones were scheduled to play Wednesday in Perth, Australia, and at other stops this week and next week, including Melbourne and Sydney. Tickets holders should keep their tickets, the statement said.

Scott was found dead in her Manhattan apartment at 10 a.m. Monday by an assistant; police said no note was found and there was no sign of foul play. She was found kneeling with a scarf wrapped around her neck that had been tied to the handle of a French door, police said.

Jagger's representative said the singer was "completely shocked and devastated by the news" of Scott's death. On Monday night, his rep also shot down a report that he and designer had recently broken up.

"The story in the New York Post re a split between Mick Jagger and L'Wren Scott is 100% untrue," said his spokeswoman, Victoria Scarfone, according to People. "There is absolutely no basis in fact to this story. It is a horrible and inaccurate piece of gossip during this very tragic time for Mick."

Jagger paid tribute to Scott on Tuesday in a statement posted on his website. "We spent many wonderful years together and had made a great life for ourselves," he said, adding, "I will never forget her."

Last month Scott, who was believed to be 49 but had not disclosed her precise age, canceled her London Fashion Week show, due to reported production delays.

Accounts filed by Scott's LS Fashion Ltd. in London show the company had liabilities that exceeded assets by 4.24 million euros ($5.9 million) as of Dec. 31, 2012.

The company's long and short-term debts totaled 6.75 million euros against assets, capital and reserves of 2.51 million euros, according to the accounts, which were filed in October.