"55 dead. Millions in queues. Crores suffering. Modiji has no time for Parliament but has time to address rock concert instead," Congress chief spokesperson Randeep Surjewala said in a tweet.
"Tragic indeed Modiji! As India suffers, bleeds and several die, your self-promotion in a rock concert is almost cold-blooded... Self-styled 'Rock Star' rocks India's poor to misery, evades the Parliament & addresses Rock Concert via video. Way to fight black money," he said in other tweets.
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Modi appeared in a video address to thousands of people who gathered in suburban Bandra Kurla complex in Mumbai for Global Citizen Festival.
The festival featured performances by international as well as Indian celebrities.
Apart from Coldplay, Jay-Z, Demi Lovato and The Vamps, Amitabh Bachchan, Shah Rukh Khan, A R Rahman, Ranveer Singh and Katrina Kaif were among the performers.
"India stands in lines, poor languish in queues for withdrawing their own money. Modiji addressing Coldplay rock concert," Surjewala said.
Modi is absconding from Parliament, refuses to face the House despite the fact that the Rajya Sabha has been demanding a reply from him, he said.
"The government should be accountable to Parliament, it is unfortunate for the country that Modi doesn't feel the need to address the House," he said.
Later, replying to a question on Priyanka Gandhi's involvement in campaigning for the Uttar Pradesh Assembly election, Surjewala said the final call will be taken by the party, President and Vice-President.