India's Supreme Court has overturned an order by a lower court and permitted a Hindu woman who had converted to Islam to live with her Muslim husband, a man federal investigators accused of being a recruiter for militant group Islamic State in an incident authorities had called "Love Jihad."

The phrase "Love Jihad" has been adopted by right-wing Hindu fringe groups that accuse Muslim men of engaging in a conspiracy to turn Hindu women away from their religion by seducing them.

The Supreme Court issued the ruling late last week, reinstating the marriage of the 24-year-old woman who had converted to Islam and changed her name from Akhila to Hadiya.

"The court has no right to annul marriage between consenting adults," said three judges of the Supreme Court, headed by the Chief Justice of India, Dipak Misra, in an interim order.

The National Investigation Agency (NIA) had told the high court in the southern state of Kerala that Hadiya was brainwashed by a Muslim man with direct links to Islamic State.

In response, the Kerala high court had annulled Hadiya's marriage, placing her in the custody of her father after the prosecutors said they feared for her well-being.

In a submission to the high court, Hadiya rejected the allegations against her husband by the anti-terror investigations agency, before appealing against the decision to the Supreme Court.

The Supreme Court allowed the agency to continue its investigation, begun in 2015, of the alleged radicalization of young Hindus in Kerala, which sends tens of thousands of workers to the Middle East, as a potential hotbed for Islamic State recruitment.

Muslims make up about 14 percent of India's population of roughly 1.3 billion, while Hindus account for more than 79 percent, the most recent census shows.