The clashes first broke out on Sunday, between protesters in favour of a controversial new Indian citizenship law and those against it.
The violence has taken on religious overtones, with Hindu and Muslim groups fighting each other.
The clashes have come during US President Donald Trump's first official visit to the country.
The violence is centred on Muslim-majority neighbourhoods in north-east Delhi - about 18km (11 miles) from the heart of the capital, where Mr Trump has been holding meetings with Indian leaders, diplomats and businessmen.
The Citizenship Amendment Act (CAA) - which critics say is anti-Muslim - has sparked massive protests since it was passed last year, and some of those have turned violent. But the demonstrations in Delhi have been peaceful until now.
When asked about the violence during a press briefing, Mr Trump evaded the issue, saying the incident was "up to India" to handle.
However, he said he had brought up the issue of religious freedom in the country and was impressed by the government's response.
Correspondents say the current unrest is an embarrassment to Prime Minister Narendra Modi as it has taken the spotlight away from Mr Trump's visit.
BBC reporters in north-east Delhi saw Hindu mobs throwing stones and shouting slogans, with some in the crowd shouting "shoot the traitors".
Our correspondent Yogita Limaye saw plumes of smoke rising from a tyre market that has been set on fire.
In another incident on Tuesday afternoon, a mosque was vandalised in the Shahadra area. Widely shared footage showed men trying to rip the crescent from the top of the minaret.