Sharma, Deputy Leader of Congress in Rajya Sabha, told PTI that the SPG had to take Gandhi out by an alternate vehicle as the alleged attackers had surrounded the vehicle of the Congress Vice President as well.
The "attack" took place some distance away from the place where the meeting was held at the varsity campus with the ABVP activists using "cover of the darkness," he claimed.
The former Union Minister said he was a "few steps" behind Gandhi.
He said his PSO has lodged a complaint with police.
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Meanwhile, the Congress termed the alleged attack, which it said was carried out by a "sharp weapon", as a "black day" in country's democracy.
"This is a black day for India's democracy when Deputy Leader of Opposition in Rajya Sabha was publicly attacked with a sharp weapon by government-protected activists. We condemn the attack in strongest possible terms," AICC spokesperson Randeep Surjewala said.
He asked Prime Minister Narendra Modi and BJP President Amit Shah to take against the culprits and also give an explanation on the attack, as law and order is the responsibilities of the government and Delhi Police.
"Prime Minister and BJP President owe an explaination...We want to ask the Prime Minister whether law and order is not his and Delhi Police's responsibility," he said.
"Will Prime Minister now take action against those goons and hooligans...Will Modi take action against Delhi Police who failed to protect and provide security.
Meanwhile, ABVP rubbished the allegations, saying its members did not indulge in any such activities.
"They were peacefully registering their protest against the presence of politicians on the campus which has politicised the whole issue," ABVP leader and JNUSU Joint Secretary Saurabh Kumar Sharma said.