Shiv Sena leader Uddhav Thackeray tweeted that he agreed with Gandhian Anna Hazare that the election result was a defeat for Modi.
"Delhi has shown that tsunami is bigger than a wave...It is a message to those who lord over Delhi," Thackeray said.
West Bengal Chief Minister and Trinamool Congress leader Mamata Banerjee, with whose party BJP has been having a running battle, said "arrogance and political vendetta have been defeated today" and that BJP's "balloon has burst".
Her party spokesman Derek O'Brien said the message from the Delhi polls was "Bhaag (run) Modi Bhaag".
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BJP's Tamil Nadu ally PMK said the reason for AAP's landslide victory was that people were yearning for change due to "corruption" in government administration.
JD(U) leader Nitish Kumar said the poll outcome in Delhi was a referendum on Modi and "it reflects the mood of the country".
In an apparent attack on Modi, he said, "Hawabazzi se kaam nahi chalega (things will not work only on the basis of lofty talks).... Astonishingly in such a short span of nine months of Narendra Modi government, the mood of people is changing against him."