Nearly 600,000 Indian men who have sexually harassed or taunted women received a text message from police over the New Year reminding them to be on their best behaviour.

"You and your phone are still under observation. Hope your conduct is upright now. We wish you a Happy New Year," said the greeting from police in the northern state of Uttar Pradesh.

The messages were sent to "Eve-teasers" - the South Asian term for the sexual harassers of women - on Thursday.

"The message to Eve-teasers, or pesky callers, is a reminder that the police have their record. It is meant as a deterrent. We are trying to tell them that any attempt to trouble women and create mischief will prompt strict action," said senior police officer Navniet Sekera, who heads a telephone helpline for women.

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Sekera said that 500,000 women who have complained about harassment would also be sent messages, assuring them that the police were available to help them should they need it.

Uttar Pradesh is India's most populous state, accounting for 200 million of India's 1.2 billion population.

Sexual harassment is a major problem in India and many cases are reported in the country during festivals and New Year celebrations.