Muslims make up about 15% of India's 1.3 billion people, most of whom are Hindu, and marriages between the two communities are still taboo in some regions.
Tanishq, a jewellery firm and unit of the Tata-controlled Titan Company Ltd., released the advertisement in its "Ekatvam", or oneness campaign, showing a Hindu bride and her Muslim in-laws holding a baby shower in the Hindu tradition.
On Wednesday, staff at the Tanishq jewellery store in the city of Gandhidham in western Gujarat state told Reuters they had posted an apology outside the store following hundreds of threatening calls.
"The Tanishq ad appearing in media today is shameful," read Monday's note, written in Gujarati, the state language. "Gandhidham Tanishq seeks forgiveness from the entire Hindu community of Kutch district."
Although some people had gone to the store seeking an apology for the advertisement, police official Mayur Patil told Reuters, there were no physical threats.
"They did get a lot of phone calls because of the ad, but there has been no attack or ransacking," added Patil, a police superintendent in the area. "Police are present at the store, and the store is functioning."
Calls to boycott the company over the advertisement were trending on social media on Tuesday, with some people accusing it of promoting "Love Jihad", a reference to the idea of a conspiracy by Muslims to forcibly convert Hindu women.
In a statement late on Tuesday, Tanishq said it withdrew the film due to "hurt sentiments, and the well-being of our employees, partners and store staff".
The withdrawal has also provoked criticism that the company is pandering to extremists.
"Its capitulation points to the pervasive atmosphere of fear and intimidation that some have unleashed in the country," said Shashi Tharoor, a prominent opposition lawmaker.
"Never thought I'd see the day when purveying communal hatred is the new normal."
Founded in 1868, Tata is one of India's largest and well-known companies, with dozens of businesses spanning chemicals to consultancy.
At the last general election in 2019, Tata was the largest donor to Prime Minister Narendra Modi's Bharatiya Janata Party, public filings show. It was also the biggest donor to the main opposition Congress party.
Modi's critics say India's long-standing tradition of celebrating diversity has come under attack since the Hindu nationalist BJP won power in 2014. The party denies this, saying it has empowered minority groups.
In 2019, an advertisement for Unilever's detergent Surf that promoted Hindu-Muslim unity also triggered a backlash.
(This story is refiled to correct byline, no changes to text)
(Reporting by Alasdair Pal in New Delhi and Sumit Khanna in Ahmedabad; Editing by Michael Perry and Clarence Fernandez)
By Alasdair Pal and Sumit Khanna