Several people have been hospitalised in Austria after using suspected fake versions of Novo Nordisk's diabetes drug Ozempic, the country's health safety body says, the first report of harm to users as a European hunt for counterfeiters widens.

The patients were reported to have suffered hypoglycaemia and seizures, serious side effects that indicate the product contained insulin instead of Ozempic's active ingredient semaglutide, the health safety regulator BASG said on Monday.

Austria's criminal investigation service warned on Monday that fake injection pens may still be in circulation.

The European Medicines Agency (EMA) last week warned about the existence of such pens falsely labelled as Ozempic.

The Danish maker of the drug, Novo Nordisk, had flagged a surge in online offers of counterfeit Ozempic as well as its weight-loss drug Wegovy, both based on semaglutide.

The company has been scrambling to boost output to catch up with overwhelming demand.

"It appears that this shortage is being exploited by criminal organisations to bring counterfeits of Ozempic to market," said BASG.

When asked to comment on the Austrian cases, Novo said in a statement it was investigating and reporting every counterfeit case that comes to its attention.

It reiterated that it had boosted efforts to monitor and take down illegal online offers.

"We recognise the limitations of this exercise and are conducting physical investigations where warranted," Novo said, adding this at times involved specialised firms "on the ground" to help authorities track down counterfeiters.

Austria's BASG did not provide an exact number of people harmed by the fake Ozempic, or say how long-lasting the adverse effects would be on their health.

The organisation running the European Union's Medicines Verification System, which conducts digital surveillance of drugs dispensed by pharmacists, on Tuesday confirmed the EMA's finding that no fakes had emerged in retail pharmacies.

The EMA and authorities in Germany and the United Kingdom, including prosecutors in southwestern Germany, have been investigating a case where bogus injection pens with German labels in genuine Ozempic packaging were sold from a wholesaler in Austria to Germany, and from there, on to two UK wholesalers.

BASG said it would not comment further on the case, to protect the investigation.