Sweden's Prince Daniel said his wife, Crown Princess Victoria, has given birth to their first child, a baby girl.

Daniel said the child, who is second in line to the throne, was born at 4.26am local time today at the Karolinska University Hospital in Solna, a suburb of Stockholm.

He said mother and child are doing well.

Victoria married Daniel, a commoner and her former personal trainer, in June 2010.

In August last year, the Royal Court announced that Victoria was pregnant and expected to give birth in early 2012.

Victoria, 34, is next in line to the throne held by her father, King Carl XVI Gustaf, since 1973.

The Swedish monarch is primarily a figurehead, representing the country as the head of state but without political power.

The baby girl - who was born 20in long and weighed 7.23lb - will be groomed to one day become the country's figurehead monarch.

"When I left the room the little princess was sleeping on her mother's chest and they were looking very cosy," an emotional Daniel told reporters. "The little daughter and the crown princess are doing very well."

Daniel said he was "pretty nervous" during the birth and that he cut the baby's umbilical cord. The girl's name will be announced later this week, he said.

Sweden changed the constitution in 1980, three years after Princess Victoria was born, to allow the eldest heir to inherit the throne regardless of gender. Before that female heirs were excluded.

She is widely admired by Swedes for being down-to-earth and unassuming. It is not uncommon to see her and Prince Daniel venture out of their lakeside palace for a stroll in a nearby public park, with security guards in tow.

Dr Lennart Nordstrom, who was present during the delivery, said there were no complications. The royal couple had specifically requested that they should not receive any special treatment, he said.

"Both the crown princess and Daniel have been adamant that they should receive the same care as everyone else," Dr Nordstrom said.

The royal family in general, and Victoria in particular, are popular in Sweden, which helps explain why the centuries-old monarchy has survived even though the concept of inherited privilege runs counter to the egalitarian character of modern Swedish society.

However, voices calling for a republic have been emboldened in recent years after the scandal surrounding an unauthorised biography of the king in 2010, with claims of seedy nightclub visits and an extramarital affair.

A close friend of the king caused him further embarrassment when he was caught on tape negotiating with mobsters in an apparent attempt to keep unflattering information about the king's entourage from the public eye.

The Swedish monarchy rests on traditions stretching back to the end of the Viking age, more than 1,000 years ago, but the current dynasty was founded in 1810, when French marshal Jean Baptiste Bernadotte was elected as successor to the throne.

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