"Much indicates that there is an outbreak of Legionnaires disease in the Sarpsborg and Fredrikstad area (east of Oslo)," the agency said in a statement.
Five people have been infected with the Legionella bacteria since mid-June, and one of them died at the beginning of this month with the second succumbing last Friday, it added.
"So far we have confirmed that two people were infected with the same bacteria strain. This indicates that other cases could also be linked and that there therefore is an outbreak of Legionnaires disease," the statement said.
All of those infected were over 50 years of age and the first man to die had been suffering from a previous life-threatening disease, the public health institute said, adding that it had yet to identify the source of the infection.
The two towns at the centre of the current possible outbreak were also the scene of a 2005 Legionnaire's epidemic that killed at least 10 people.
Authorities "have investigated showers in the patients' homes and taken samples from installations in the municipalities that could be spreading the Legionella bacteria," the agency said.
Following the 2005 outbreak, authorities "have a good overview over possible sources ... All known installations have been disinfected or will be in coming days," it added.
Legionnaire's disease causes high fever, a dry cough, lung congestion and subsequent pneumonia. It is commonly spread through contaminated air conditioning and public water systems and is treated with antibiotics.