A senior leader of India's ruling Bharatiya Janata Party (BJP) has said that Muslims living in the country should give up consuming beef.
Manohar Lal Khattar, Chief Minister of Haryana state, said the cow "is an article of faith" in India.
Most states ban the slaughter of cows, which is considered a sacred animal by India's majority Hindu community.
The beef ban has provoked outrage, with many questioning the government's right to decide what is on their plate.
It has also been criticised by many as beef is cheaper than chicken and fish and is a staple for the poorer Muslim, tribal and Dalit (formerly untouchable) communities.
The main opposition Congress party has criticised Khattar's remark - party spokesperson Rashid Alvi said Khattar "has no right to remain chief minister".
"Muslims can continue to live in this country, but they will have to give up eating beef. The cow is an article of faith here," Khattar told The Indian Express newspaper.
The chief minister said "freedom of one person is only to the extent that it is not hurting another person".
"Eating beef hurts the sentiments of another community, even constitutionally you cannot do this. The constitution says you cannot do something that offends me, I cannot do something that offends you," he said.
"They can be Muslim even after they stop eating beef, can't they? It is written nowhere that Muslims have to eat beef, nor is it written anywhere in Christianity that they have to eat beef."
India's federal government, also headed by BJP, has come under increasing pressure from Hindu hardliners to do more to protect cows.
Last month a 50-year-old Muslim man was killed by a Hindu mob in Uttar Pradesh over rumours that his family had been storing and consuming beef at home. His 22-year-old son was seriously injured in the attack.
Mr Khattar said the killing was a "result of misunderstanding" and that "both sides" had committed wrongs.
"It should not have happened - from both sides. But I say that attacking and killing the person was also wrong," he said.
Despite the slaughter of cows being widely banned, India ranks as the world's top beef exporter thanks to buffalo meat exports, according to a report by the US department of agriculture.
It is expected to export 2.4 million tonnes of beef in 2015, against Brazil's 2 million tonnes.