"Those who are here to push around people must go home. Now please maintain calm and walk silently," an angry Priyanka Vadra told the crowd.
"Think about the cause for which you have come here," she said, reported news agency PTI.
Rahul Gandhi was protesting against the "silence" of Prime Minister Narendra Modi over the rapes and to seek justice for the victims.
Several senior Congress leaders, including Ahmed Patel, Ghulam Nabi Azad and Ambika Soni, joined the Thursday midnight candle-light protest. People also gathered at the place in sizeable numbers to express their support.
The Congress President tweeted on late Thursday night about his intention to go on a candle march.
Like millions of Indians my heart hurts tonight. India simply cannot continue to treat its women the way it does.
- Rahul Gandhi (@RahulGandhi) April 12, 2018
Join me in a silent, peaceful, candlelight vigil at India Gate at midnight tonight to protest this violence and demand justice.
Priyanka Vadra's husband Robert Vadra was also present in the protest march to the India Gate. He said the country needs a change where women could feel safe.
Rahul Gandhi was called out on social media about the girl's horrific ordeal. He broke his silence and wondered how anyone could "protect the culprits of such evil? What happened to [her] #Kathua is a crime against humanity. It cannot go unpunished."
A huge crowd gathered for the march where slogans were raised against the Narendra Modi-led BJP government.
(With inputs from PTI and IANS)
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