Sena Minister Eknath Shinde, who holds Public Undertaking portfolio, made the offer to resign at a civic poll rally in Kalyan after the Sena chief lashed out at Fadnavis.
Thackeray warned that if the "BJP continues its arrogance" Sena will not hesitate to pull out of the alliance.
As soon as Thackeray finished his speech, Shinde rushed to his leader who was present on the stage saying that he was quitting as he could no longer suffer the "humiliation" being meted out to Sena cadres by BJP which was "misusing" official machinery.
Reacting to Shinde's open offer to quit his cabinet, Fadnavis, who was also campaigning for his party in a nearby area, dubbed it as "drama".
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"We have seen on television a cabinet minister making allegations and offering resignation. This is nautanki (drama)," Fadnavis said.
The BJP-Sena slanging match has become shriller after the two parties decided to contest separately the polls to Kalyan Dombivili Municipal Corporation, going to vote on November 1.
Taking a cue from his leader, Shinde made an emotional speech saying he could no longer tolerate the humiliation being heaped upon Sena workers and he was submitting his resignation.
"I agree with the views of Shinde and would like to warn the chief minister that enough is enough and we are losing our patience on the misuse of government machinery at every stage. They (BJP) clearly see their defeat and hence make use of all kinds of methods to crush us," Thackeray said.
"Let there be a fight over principles and on the basis of the work done but this kind of misuse of power will not be tolerated at any cost," he said.
He asked the Sena workers to be alert in the next two days till the the civic polls end.