Croatia's conservative Most party handed 82 boxes of papers in to parliament on Monday carrying the signatures of 410,533 people calling on the government to hold a referendum on whether to abolish COVID-19 certificates.
The government must check the signatures, and if they are found to be valid, the date for a referendum can be set.
Croatia has one of the European Union's lowest vaccination rates, with around 55% of its population inoculated against COVID-19, ahead of only Bulgaria, Romania and Latvia.
The EU's newest member state reported 1,823 new coronavirus cases on Monday, a significant drop from the 16,017 reported last Tuesday.
Most MP Nino Raspundic said the initiative came about after a study showed that even people who are fully vaccinated can pass on the virus.
"This study proved certificates are useless and that testing is the only way to ensure that there will be no infections in hospitals or homes for the elderly, for example," he told reporters.
"Even countries that have introduced COVID-19 certificates earlier than Croatia have rising number of cases."
Croatia introduced COVID-19 certificates last year, but unlike their EU peers not for restaurants and cafes. The certificates are needed to enter public buildings including courts, various ministries and parliament.
(Reporting by Ivana Sekularac; Editing by Hugh Lawson)
