A politician from India's main opposition party has been arrested for allegedly making an anti-Muslim speech during a recent election rally.

At least 10,000 supporters of Varun Gandhi shouted pro-Hindu slogans at police as he was arrested in the northern Uttar Pradesh state on Sunday.

Gandhi, a grandson of the late Indian prime minister, Indira Gandhi, is alleged to have made inflammatory comments while campaigning as a candidate of the Hindu nationalist Bharatiya Janata Party (BJP) earlier this month.

"Varun will remain in judicial custody in Pilibhit jail till Monday when his bail plea will be decided", Mani Ram Rao, the investigating police officer in the case, said.

India's independent election commission has demanded that the BJP drop Gandhi as a candidate, but the BJP has defended Gandhi's right to express his views.

During a speech by Gandhi, which was aired on television, he is seen apparently making offensive remarks against Muslims.

Criminal charges were filed against him after the election commission reviewed the footage.

Gandhi has said footage of his speech was doctored in a political conspiracy to tarnish his image.

"I am ready to go to jail. And I have come here to boost the morale of my people," Gandhi said before his arrest.

"I believe in whatever I have said."

Hindu-Muslim tensions

The BJP has been accused in the past of stoking tensions to appeal to its large Hindu voter base. Muslims make up around 13 per cent of India's 1.1 billion population.

Many opinion polls show the BJP-led main opposition alliance trailing the Congress-led ruling coalition.

Varun Gandhi is the son of Sanjay Gandhi, Indira Gandhi's younger son who was killed in a plane crash.

Although he is a descendant of the influential Nehru-Gandhi dynasty, Varun Gandhi belongs to a side of the family that has disowned them.

Three out of India's 14 prime ministers belong to the Nehru-Gandhi family, including the first, Jawaharlal Nehru.