Most of the new cases have been recorded in the northern province of Norrland and in Stockholm and primarily concern outbreaks of the flu in schools.
To date 1,778 cases of the new A(H1H1) virus have been recorded since the outbreak began.
"It is mainly the parents that we are most concerned for. They are the ones that will get the sickest. I don't think it will be long before we get one or more serious cases," said Annika Linde at the institute.
Sweden launched a mass vaccination programme in a bid to control the flu pandemic on October 12th. Several of the new cases are connected to the vaccine.
Five cases of allergic reactions have been reported by patients after having been given the vaccine. The patients required hospital care although symptoms were eased after treatment.
Around 200 reports of people suffering side effects after receiving the vaccine have so far been reported to the Swedish Medical Products Agency (Läkemedelsverket).
The most common complaints are pains in arm in the vicinity of the injection, as well as muscle and joint pain.
Other complaints include a general feeling of illness and mild influenza symptoms.
Those suffering allergic reactions have complained of dizziness, rashes, itching and pain in the chest.
Of the around 200 cases, 100 have come from personnel employed within healthcare, one of the prioritized groups, and the rest from the general public.
"This do not differ from what we already know nor what we had expected. The general picture is of mild influenza symptoms and localized symptoms from the injections," said Gunilla Sjölin Forsberg at the agency.
From previous studies it is known that there are likely to be a large number of unreported cases of side effects. The actual figure could be ten times as high.