ATHENS (Reuters) - Greece's far-right Golden Dawn party hit back at plans for an anti-racism law on Tuesday by submitting its own draft bill to fight "racism against Greeks" by jailing all illegal immigrants.

Members of Greece's ruling coalition have been squabbling for days over the details of legislation aimed at curbing a rise in attacks on migrants.

The law is widely seen as an attempt to rein in Golden Dawn, which has tapped into widespread anger against austerity and corruption to become the third most popular party in the country.

Golden Dawn emerged from obscurity and entered parliament for the first time last year, winning supporters with its free food handouts only for Greeks and fierce rhetoric blaming migrants for crime.

It has denied having any involvement in the attacks.

"The established parties have been competing for days: which one is going to submit the toughest anti-racism bill to make delinquency permanent and turn Greeks into a minority in our own country," Golden Dawn said in a statement outlining its bill.

"The only racism that exists at this moment in the country is racism against Greeks."

Golden Dawn said its bill proposed jailing anyone who entered the country illegally - even if they later obtained a legal permit - for at least three months and a sentence of at least 10 years if they subsequently committed a felony.

"The foreign criminals who have killed our compatriots have been convicted for serious crimes but are still free," it said. "Golden Dawn's proposal will immediately solve this problem by sending every illegal immigrant who violates the law to prison."

The ruling coalition's junior partners - the Socialist PASOK and the Democratic Left - have jointly submitted a draft anti-racism bill that toughens penalties for inciting racial hatred, denying the Holocaust or carrying out attacks.

The conservative New Democracy party says it plans to amend existing racism laws.

Parliament will vote on those and any other proposals in the coming weeks. Golden Dawn has 18 seats in the 300-member parliament, meaning its bill has virtually no chance of passing.

(Reporting by Renee Maltezou; Editing by Deepa Babington and Andrew Heavens)