In Aligarh, a group called the Hindu Jagran Manch has warned schools against celebrating Christmas, saying they could do so "at their own risk".
In a letter to schools, the group has demanded that children should not be asked to bring gifts or participate in Christmas programmes.
Such activities, says the group, are "a step towards forced conversions" of Hindu students. "We will decide on a course of action on receiving their (the schools') response," Sonu Savita, city president of the Hindu Jagran Manch, was quoted as saying by news agency Press Trust of India.
In Agra, two groups, the Hindu Jagaran Manch and Vishwa Hindu Mahasangh, have told reporters that they want to register "peaceful yet vociferous" protests against what they call "obscene behavior" during the New Year celebrations in hotels and restaurants.
The police say they are taking precautions to ensure that the festivities go smoothly. An alert has been sent to all districts and officers have been asked to "take strict legal action" against those indulging in intimidation, PTI quoted senior police officer Anand Kumar as saying.
The state government denied knowledge of these threats. "The government has clear policies that all religions must be respected. People are free to celebrate festivals of any religion," Deputy Chief Minister Dinesh Sharma said on Tuesday.
Last week, a priest and four seminarians were arrested for alleged forced conversions after they organised a pre-Christmas event in Satna, Madhya Pradesh. The priests said when they were taken to a police station, activists of the Bajrang Dal, another right-wing organization, who had filed the complaint, thrashed them.
Recently, Amruta Fadnavis, the wife of Maharashtra Chief Minister Devendra Fadnavis, was heavily trolled on social media for promoting a Christmas-themed charity event. Ms Fadnavis had to put out a clarification, where she said, "Love, sharing and empathy have no religion - let's accept all positivity around us and stay away from negative thoughts and demotivating energies".