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.