The US President carried out a whirlwind 36-hour first state visit to the country, personally led by Indian prime minister Narendra Modi.
India and have seen months of protests over a new citizenship law that fast-tracks naturalisation for foreign-born religious minorities of all major faiths in South Asia except Islam, a law Prime Minister Modi has defended.
It is thought the most recent rioting started as a result of President Trump's visit but is a continuation over the same issue.
India has been rocked by violence since its parliament approved the citizenship law in December.
Authorities said the death toll from the most recent clashes is expected to rise as hospitals struggle to cope with dozens of injured people.
New Delhi's top elected official, chief minister Arjind Kerjiwal, called for the government of Indian prime minister Narendra Modi to send the Indian army to areas in a north-eastern corner of the capital affected by the riots.
On Wednesday, Mr Modi broke his silence on the clashes, tweeting that "peace and harmony are central to (India's) ethos. I appeal to my sisters and brothers of Delhi to maintain peace and brotherhood at all times.."
The clashes escalated between Hindu mobs and Muslims protesting against a contentious new citizenship law. The legislation fast-tracks naturalisation for foreign-born religious minorities of all major faiths in South Asia except Islam.
Although post-mortem examinations are pending, medical officials at the Guru Teg Bahadur Hospital said some of those who were killed had bullet wounds.
Others arrived to hospital with gunshot or stab wounds.
A resident of Mustafabad, one of the affected areas, Rouf Khan said mobs were wielding iron rods, bricks and bamboo sticks.
The 43-year-old said rioters attacked the homes of Muslims. He said: "After forcing inside the homes, they went on a rampage and started beating people and breaking household items.
Mr Khan said he and his family had to run out of fear and take shelter inside a nearby mosque.
Mr Trump told reporters on Tuesday that he had heard about the violence, but had not discussed it with Mr Modi.
The president instead praised a mega-rally Mr Modi and his Hindu nationalist Bharatiya Janata Party-led government organised for him.
The event in the prime minister’s home state of Gujarat drew an estimated 125,000 people.
Opponents of the new legislation said the country is moving toward a religious citizenship test.
Mr Trump, in keeping with his tendency not to criticise the leaders of countries he has visited, declined to comment on it.
"I don’t want to discuss that. I want to leave that to India and hopefully they’re going to make the right decision for the people," he said.
Television images from New Delhi showed streets littered with mangled remains of vehicles, rocks and burned tyres.
The worst-hit areas of Chand Bagh, Bhajanpura, Gokulpuri, Maujpur, Kardampuri and Jaffrabad reportedly saw pitched battles between rival groups who also hurled petrol bombs and opened fire on Monday and Tuesday.