(Adds prime minister's comments)

MADRID, March 27 (Reuters) - Spain is to investigate whether a new party applying to stand in May regional elections is a vehicle for a banned Basque separatist party.

Batasuna, which is banned for not renouncing violence, said in an interview with Reuters last week it would do everything possible to take part in the elections on May 27. A deadline for electoral registration is only weeks away.

The new party is called Abertzale Sozialisten Batasuna (ASB), meaning Unity of Basque Socialist Nationalists. It will use "exclusively democratic political means" to achieve independence and socialism, Basque language newspaper Gara reported on its Web site.

Spain's interior ministry said it would ask the public prosecutor to investigate if the party was legal.

Prime Minister Jose Luis Rodriguez Zapatero told a television debate that the interior minister saw "signs of illegality" in those backing the party, its name and its statutes.

"Nobody is going to run at the next local elections ... if they haven't complied with the political parties law, to the dot," he said.

The interior ministry said in a statement that party backers might have direct links with illegal organisations and parties, adding: "The name used by the political organisation seems to have a ... similarity with illegal political parties Batasuna and Herri Batasuna."

Spain says it wants Batasuna to put up candidates in regional elections in the Basque Country but it must clearly condemn violence first.

Basque nationalists have said they expect Batasuna will come up with a formulation of words that will satisfy Madrid's demands. However, the ruling Socialist party is under pressure from its conservative opposition and a large swathe of the Spanish public not to cede ground to ETA and its supporters.

Batasuna was banned in 2002 for its links to ETA guerrillas who have led a violent campaign for an independent Basque Country over nearly four decades.

In December the government said it was ending a peace process with ETA after a bomb at Madrid airport killed two people.

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