Prince Frederik flies to New Zealand on separate plane to meet Princess Mary

Meanwhile, Frederik, 55, just arrived with their second eldest child Princess Isabella, 16, on a separate flight.

Prince Christian, 18, has stayed in Denmark to complete his education.

The Danish royals have not been photographed together yet on their family holiday.

This getaway comes as Crown Princess Mary makes a low-key visit to her home country Australia every year.

The future Queen of Denmark, who is from Tasmania, usually makes several public appearances during her Christmas holidays.

But she has barely been seen since she landed in Sydney on December 6 without her husband.

Mary's solo visit led some fans to speculate she was hiding after Prince Frederik was photographed with a Mexican socialite last month.

Photos published in November showed Prince Frederik out for the evening in Madrid with the Mexican socialite Genoveva Casanova.

The Spanish magazine Lecturas published the photos and alleged the pair were having an "affair".

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Casanova denied the "malicious" rumours that she was romantically involved with the heir to the Danish throne.

Since the photos emerged, neither Princess Mary nor Prince Frederik have issued any statement.

The pair put on a united display with King Felipe and Queen Letizia of Spain, who were visiting Denmark on a State Visit at the time.