The right wing Independent Greeks party has made an official proposal in Parliament to abolish a citizenship law granting migrants greater rights, Skai reported on Monday.
The far right Golden Dawn party has made a similar proposal, Skai said.
Passed by PASOK socialists in 2010, the law allows second-generation immigrants whose parents have been living in Greece legally to apply for Greek citizenship.
New Democracy leader Antonis Samaras has in the past said he wants to repeal the law, saying it is a magnet for undocumented migrants who see it as an opportunity to obtain legal status in a European Union country.
PASOK and Democratic Left, the two other parties in the conservative-led coalition government, oppose any changes to the legislation.