During his show in the US, Vir Das described a country of two sides where people “worship women during the day but gang rape them at night”.
In response to the strong backlash, he called it “satire about the duality of two very separate Indias”.
Others have shown support for the comic, who received a standing ovation.
The monologue was performed in Washington DC on 12 November during his current world tour.
A seven-minute video was uploaded online and quickly went viral.
“I come from an India where the AQI (air quality index) is 9,000 but we still sleep on the roof and look at the stars,” Mr Das, 42, told the sold-out crowd.
“I come from an India where we take pride in being vegetarian, and yet run over the farmers who grow our vegetables,” he continues, referring to a car, owned by a government minister, allegedly being driven into protesting farmers last month, killing at least eight people.
A Delhi spokesman for the ruling right-wing BJP political party said he had lodged a complaint with the police, accusing Mr Das of making “derogatory statements against women and India”.
“They were made in the US and malign the image of our country internationally. I want police to conduct an investigation,” said Aditya Jha.
Mr Das also faced criticism from some fellow performers, including actress Kangana Ranaut who called Mr Das’s actions “soft terrorism” in an Instagram story, adding that “strict action should be taken against such criminals”.
However several opposition politicians stood up for the comedian.
Writing on Twitter, Shashi Tharoor, a member of the Congress Party, said Mr Das “spoke for millions” and called him a “stand-up comedian who knows the real meaning of the term ‘stand up’ is not physical but moral”.
Mr Das defended his performance, in an Instagram post that said the show was about “two very separate India’s that do different things.
“Like any nation has light and dark, good and evil within it. None of this is a secret,” he wrote.
“It ends in a gigantic patriotic round of applause for a country we all love, believe in, and are proud of,” he said, referring to the standing ovation he received.
“Please do not be fooled by edited snippets.”
The backlash against Mr Das echoes another recent case, that of comedian Munawar Faruqui who was imprisoned for more than a month for allegedly making “indecent remarks” about Hindu gods.
Mr Faruqui has since seen a series of his concerts cancelled after threats from a right-wing Hindu group.
Observers have raised concerns about freedom of the press and freedom of expression in India in recent years. Authorities, under prime minister Narendra Modi, have been accused of going after those who show the BJP party in a bad light and arresting journalists for critical reporting.
SOURCE: NEWS AGENCIES