An elderly man from the Glasgow area has become the second Briton to die from swine flu.

The 73-year-old, who had other very serious underlying health problems and has not yet been named, died at the Royal Alexandra hospital in Paisley late on Saturday night. He had been in intensive care for 15 days, health officials said.

Nicola Sturgeon, the Scottish health secretary, said: "Our thoughts are with the family and friends of the patient at this tragic and very sad time. The family have asked for the patient's identity to be kept private.

"Although it is concerning that the patient had swine flu, we are aware that the patient had very serious underlying health issues."

A family spokesman said: "Our beloved relative was private in life and we would ask that his privacy continues to be respected as we try to come to terms with our loss."

The first Briton to succumb to the H1N1 virus, Jacqui Fleming, also died at the Royal Alexandra after giving birth prematurely to her third child. She was the first person outside the Americas to die with the virus.

Fleming also had significant underlying health problems, and had been critically ill for several weeks before she died. Her baby, named Jack by her partner, William McCann, died the following day.

Health officials have repeatedly stressed that the virus appears to be relatively mild, despite its rapid transmission around the world.

The latest official figures show that 4,322 Britons have so far contracted the virus, with significant outbreaks now in Birmingham, London and the Glasgow area, but health experts believe the real figure will be much higher.

In the United States, specialists at the Centers for Disease Control in Atlanta estimate that at least one million Americans may have had swine flu and not been diagnosed, although the official figures on Friday put confirmed US cases at 27,717, with 127 deaths.

However, the virus is now spreading quickly in the southern hemisphere, where it is winter – the traditional season for flu epidemics.

In Australia, where confirmed cases stood at 3,280, four people have now died, all with underlying health problems. There have been 21 deaths reported by the World Health Organisation in Argentina and seven in Chile. The last WHO update put total cases at 59,814 with 263 deaths.