Kejriwal told NDTV in an interview that Modi was using Lt. Governor Najeeb Jung to create obstacles for his Aam Aadmi Party government to avenge the BJP's rout in the February elections in Delhi.
"He (Modi) is taking revenge against the people and the Aam Aadmi Party because of the loss (in Delhi). He cannot be a good prime minister," Kejriwal said.
Admitting that people had voted for Modi nationally and for the AAP in Delhi, Kejriwal said: "He (Modi) should run the country and let us run Delhi."
The AAP leader, who led his party to a sweeping win, accused Jung of behaving like a "polling agent" of the Bharatiya Janata Party.
"The Lt. Governor's house has become the second headquarters of the BJP."
Jung and Kejriwal's government have been locked in a bitter row over administrative issues in the Delhi administration, with the Lt. Governor asserting his authority in select areas.
The chief minister said Jung does not respond to telephone calls of Delhi Deputy Chief Minister Manish Sisodia.
Lt. Governor's house has become the second headquarters of the BJP: Kejriwal
"Manish calls him, many times, but his phone is never answered. If the watchman of (BJP president) Amit Shah calls him, he will go crawling," the chief minister said, using unusually strong words.
Suggesting that he was a mass leader, Kejriwal said the BJP leadership must realize that he was not a Rahul Gandhi.
"Narendra Modi ji must realise that I am not Rahul Gandhi," he said. Asked what he meant by that, Kejriwal smiled and said after a pause: "The message I wanted to convey has been conveyed."
The chief minister also made light of reports that the central government could stop the salaries of Delhi government officials.
"Let them do it if they can," he said, adding the AAP government was not beholden to the central home ministry, to which the Lt. Governor reports.