VIENNA (Reuters) - Less than 1% of Austria's population is infected with the coronavirus, a study published on Friday found, based on testing a representative sample of more than 1,500 people.

The first such study in continental Europe, led by pollster SORA which is known for projecting election results, aimed to provide a clearer picture of the total number of infections, given gaps in testing.

Austria's current policy is to test people with symptoms, especially if they have been to a known hotspot or in close contact with an infected person. That means many cases, such as people with no symptoms and those with no known contact to an at-risk area, go undetected.

"Based on this study, we believe that 0.33% of the population in Austria was acutely infected in early April," SORA co-founder Christoph Hofinger told a news conference. Given the margin of error, the figure was 95% likely to be between 0.12% and 0.76%.

Austrian Chancellor Sebastian Kurz, whose government commissioned the study and saw initial findings a few days ago, said on Monday that the rate of infection was around 1%. He said that disproved the idea of herd immunity - which requires widespread infection - as a viable policy option.

Austria reacted early to the outbreak in the country, closing schools, restaurants, theatres and other gathering places more than three weeks ago, and telling the population to stay home and work from there if possible.

The outbreak has remained within the health system's capacity and hospitalisations have stabilised, with the daily percentage increase in infections in low single digits. There have been 319 deaths so far.

Austria has reported 13,337 confirmed cases, roughly 7,000 of which are still active, meaning they have neither recovered nor died. The study estimated the current number of infections was more than four times that - around 28,500 people. It also excluded those in hospital, currently around 1,000 people.

The study, conducted between April 1 and April 6, in which 1,554 people were tested, did not involve antibody tests, which could tell whether a currently virus-free person was previously infected and is therefore probably immune. Future studies should involve antibody tests, the government has said.

Those studies will inform policy as Austria starts to reopen shops as of Tuesday next week.

"We must monitor whether there is a second wave and the number of infected people starts to rise again... We are still in a very, very sensitive situation. This study shows that, too. Corona is in our society," Education Minister Heinz Fassmann, whose portfolio includes research, told the news conference.

(Reporting by Francois Murphy; Editing by Kirsten Donovan)