As Donald Trump was being hosted by Indian PM Narendra Modi in western India on Monday, Hindu nationalist and communist groups held pro- and anti-US demonstrations in the capital.
One police officer was killed in the violence and at least 11 other officers injured as they were hit by rocks trying to separate rival groups.
Some local agencies reported three protesters had been killed but this could not be confirmed.
A group of Hindu nationalists held a prayer meeting in which they put a vermilion mark on the forehead of Trump’s photograph on a poster, blessing him, while a priest chanted Hindu hymns wishing Trump success in his endeavor for strong ties with India.
Elsewhere in New Delhi, dozens of supporters of the Communist Party of India carried a banner reading "Trump go back." Anti-Trump street demonstrations also broke out in the cities of Gauhati in the northeast, Kolkata in the east and Hyderabad in the south.
American dairy farmers, distillers and drugmakers have been eager to break into India, the world’s seventh-biggest economy, but talks between Washington and New Delhi appeared to have fizzled.
Also in New Delhi, police fired tear gas as clashes erupted between hundreds of supporters and opponents of a new citizenship law that provides fast-track naturalization for some foreign-born religious minorities but not Muslims.
Critics say the country is moving toward a religious citizenship test. New Delhi's highest elected official, Arvind Kejriwal, tweeted that the violence was “very distressing.”
The New Delhi television news channel said authorities deployed paramilitary forces to defuse the situation, and the clashes were trending on social media using the hashtag #DelhiBurning.