Gordon and Sarah Brown pictured after baby James Fraser's birth

A spokesman for Mr Brown said he and his wife Sarah were told in late July that Fraser may have the genetic disease and tests had now confirmed it.

He added Fraser was "fit, healthy and making all the progress that you would expect any little boy to make".

The couple have one other son, John. Their daughter Jennifer Jane died after being born prematurely in 2002.

Cystic fibrosis (CF) is a life-threatening inherited disease which disrupts the way the digestive and respiratory systems work.

Chest infections

The Sun newspaper reported Fraser had been in and out of hospital since his birth with minor chest infections.

Mr Brown's spokesman added: "Thousands of other parents are in the same position.

A child diagnosed at birth and treated immediately should remain quite well Rosie Barnes Cystic Fibrosis Trust Cystic fibrosis

"They are confident that the advice and treatments available, including proper exercise and, later, sporting activity will keep him fit and healthy.

"The NHS is doing a great job, and Gordon and Sarah are very optimistic that the advances being made in medicine will help him and many others, and they hope to be able to play their part in doing what they can to help others."

Mr Brown, who is widely tipped as the favourite to succeed Tony Blair when he steps down as prime minister, said after Fraser's birth in July: "I love being a dad. It's great fun and there's nothing more important and there's nothing I enjoy better. "

Medical advances

Cystic Fibrosis Trust chief executive Rosie Barnes said while the disease remained a "very serious medical condition", advances meant the future was much more optimistic than it used to be.

"I believe Fraser was tested at birth for cystic fibrosis so it would be diagnosed just a few weeks after he was born.

CYSTIC FIBROSIS Most common inherited life-threatening disease in UK It affects vital organs - lungs and pancreas There is currently no cure More than 7,500 people in UK have CF 70% of those are under 20-years-old Each week five babies are born with CF Average life expectancy is 31 Figures from the Cystic Fibrosis Trust

"If that test takes place it's very quick and treatment can start immediately... A child diagnosed at birth and treated immediately should remain quite well."

Ms Barnes said he would have to accept regular medical treatment. She also said that while there were people in their 20s and 30s who were waiting for lung transplants, the treatments today were not available when they were children.

Housing minister Yvette Cooper, a close friend of the Browns along with her husband, Economic Secretary Ed Balls, told the BBC Fraser was a "happy and healthy little boy".

She added: "They are a very strong and happy family, so whilst obviously, it is the same for any parent, it's not the kind of thing you ever want to happen - but they are very optimistic."

Conservative leader David Cameron, whose four-year-old son Ivan has cerebral palsy, said: "Sam and I are thinking of Gordon and Sarah and their family at this time and we send them our best wishes for the future."