ANKARA, Feb 20 (Reuters) - Deputy Prime Minister Mesut Yilmaz, who oversees relations with the EU, said on Wednesday Turkey should allow some Kurdish-language education and that lifting the ban would not erode national unity.

The European Union, which Turkey wants to join, has urged Ankara to improve cultural rights for its 12 million Kurds, but authorities fear greater freedom could encourage restive Kurds to demand more autonomy.

"People should be able to learn their parents' language if they want to," Yilmaz said in an interview with NTV television. "If it's by private means outside of official (schools), the state shouldn't block this and shouldn't forbid it."

He added, however, that Turkish should remain the official language in state schools. Under current laws, Kurdish cannot be taught in private language schools or community groups.

Yilmaz's remarks, made in an interview with NTV television, differed sharply with those by Prime Minister Bulent Ecevit, who has said Kurdish instruction is "unacceptable" and blamed separatists for organising a campaign for the ban be lifted.

Last month police detained hundreds of parents and students who signed petitions calling for Kurdish teaching.

The Kurdistan Workers Party (PKK) has waged an armed struggle for self-rule that has claimed more than 30,000 lives since 1984. Violence dropped off sharply with the 1999 capture of PKK leader Abdullah Ocalan, who ordered his followers to withdraw from Turkey and seek cultural rights for Kurds.

Asked whether separatists were using the Kurdish-language campaign to divide Turkey, Yilmaz said: "I definitely don't believe this, I do not share these fears."

"I believe just the opposite. By blocking it without any good reason you serve the PKK's propaganda. When we make this free, very few people will take advantage of it," he said.