EKRE has submitted a bill to the Riigikogu to stop party members' names from being made public saying it wants to protect people from possible political persecution.
Currently, anyone can view a person's party affiliation in the commercial register.
Henn Põlluaas, chairman of the EKRE Riigikogu faction, claimed EKRE members have faced repression due to their affiliation with the party.
"They have been fired or have not been hired or are forced to resign from EKRE if they want to keep their job. We have received a lot of these cases," Põlluaas said.
"As these lists are not public elsewhere in Europe, we thought we would follow the example of other European Union countries."
Põlluaas said it should be up to a member to decide whether they want to disclose their party affiliation or not. But it should not be on the internet for everyone to see.
EKRE Riigikogu member Paul Puustusmaa said only Estonia and Latvia have this rule.
"In other countries, it has long been understood that individuals' political views, including party affiliation, are clearly viewed as personal data. Membership of political parties, which is also disclosure of a person's political views, is incompatible with personal and social security," Puustusmaa said.
The party submitted the bill on Thursday before the spring session ended.
Editor: Helen Wright