The eurosceptic party, which has four deputies in the 151-seat parliament, and some small right-wing allies need to collect signatures from 10% of the electorate, or around 370,000 people. They will set up some 250 locations across the country to try to reach that.
The centre-right government, led by Prime Minister Andrej Plenkovic, is working to achieve euro adoption from the beginning of 2023 and hopes to get a green light from the euro zone in the first half of 2022.
Plenkovic says adopting the euro would remove currency risk, reduce interest rates, improve the country's credit rating and open the way for more investments in an economy dominated by tourism.
The eurosceptics say the economy is too weak and uncompetitive to be ready to adopt the euro and doing so would cause price rises.
According to a opinion poll released in July, a bit over 60% of voters favour adopting the common currency, which is used by 19 of the 27 EU members.
The government says a referendum is not necessary, arguing that Croats already accepted a common currency when they voted in a referendum to join the EU nearly a decade ago.
As a first step, organisers of the referendum initiative want a referendum on a constitutional change that would make replacing the kuna currency possible only by direct vote of the citizens.
"Our opinion is that the decision on such an important issue must be taken by the citizens and not by any prime minister or any government," Marijan Pavlicek, one of the key initiative organizers, told the Vecernji List daily over the weekend.
If enough signatures are collected by Nov. 7, the Constitutional Court may need to rule on whether the issue of the euro adoption was dealt with at the time of EU accession, or whether the referendum initiative has a legal basis.
($1 = 6.4645 kuna)
(Reporting by Igor Ilic; Editing by Frances Kerry)