By Rupam Jain

NEW DELHI, Oct 24 (Reuters) - Indian Prime Minister Narendra Modi on Monday waded into a controversy over a Muslim divorce law he said was destroying women's lives, drawing criticism from rivals that he was fishing for minority votes in a major state election next year.

Modi criticised the so-called "triple talaq", that allows a Muslim man to part from his wife by saying "I divorce you" three times, in a speech in the northern state of Uttar Pradesh, due to go to the polls next spring.

The prime minister's Bharatiya Janata Party (BJP) swept the state that is home to one in six Indians in the 2014 national election, and needs to broaden support outside its core Hindu base to have a chance of winning the state polls.

"The lives of Muslim women cannot be allowed to be destroyed by 'triple talaq,'" Modi told a rally in the town of Mahoba. "It is the responsibility of the government and people of the country to give justice to Muslim women."

Muslim women in India have long demanded a ban on the practice, banned in most Islamic countries but allowed by the Indian constitution.

The national Law Commission recently sought public views on whether to abolish the practice, triggering a debate between politicians and religious leaders.

More than 24 Muslim women's rights groups, who wrote to Modi demanding reforms to Muslim laws on divorce and polygamy, have also filed a petition in the Supreme Court.

Modi's political opponents and Muslim religious leaders accuse the 66-year-old prime minister of trying to appease women in the Muslim community for electoral gains.

"'Triple talaq' was Modi's new political tool to break up the Muslim vote," said Asaduddin Owaisi, the leader of a Muslim political party, the All-India Majlis-e-Ittehad-ul Muslimeen.

"The prime minister can stoop to any level. He now wants Muslim women to vote for him as he is desperate to win Uttar Pradesh," Owaisi told Reuters.

Muslims make up 19 percent of the population of Uttar Pradesh - above the national average.

Many feel disenfranchised by Modi and his hardline Hindu supporters, while some have been attacked by vigilantes for consuming beef or skinning cows, which Hindus regard as sacred.

The Rashtriya Swayamsevak Sangh, a Hindu-nationalist grassroots movement that backs Modi and the BJP, chronicled hundreds of cases of triple talaq in a recent report.

Most involved women from poor families, it said, whose husbands divorced them by telephone and did not honour their obligation to pay maintenance.

"These religious rules are barbaric and totally unacceptable. We want the government to protect Muslim women," said a senior leader of the RSS in New Delhi.

(Editing by Douglas Busvine; and Clarence Fernandez) ((Rupam.Nair@thomsonreuters.com; +91 11 4178 1006;))