Australia on Monday reported three new swine flu-related deaths, taking the total to 35, as more than 1,000 new infection cases were reported in just 24 hours.
New South Wales chief health officer Kerry Chant said three men aged between 47 and 65, all with pre-existing medical problems, died in the state in recent days.
"Unfortunately, although most people have a relatively mild disease, some people, especially those with underlying conditions, will have more severe disease and we can expect further deaths as winter progresses," she said.
Health authorities said cases had jumped 1,100 to 13,178 nationwide and warned that with 95 patients in intensive care, the death toll was likely to climb.
Chant urged pregnant women, Aborigines and those with chronic medical conditions to be "extra vigilant" if they developed flu-like symptoms.
Health Minister Nicola Roxon last week said 6,000 could die in Australia in a "worst-case scenario" if no action was taken against the virus, which has killed more than 400 people worldwide.
Federal authorities believe A(H1N1) infections will peak next month and have ordered 21 million doses of swine flu vaccine, enough to inoculate the entire population, for a mass immunisation program expected to begin in October.