The party also asked why these BJP workers were not similarly agitated when Kamat and other Congressmen demanded criminal action against Sushma Swaraj and Vasundhara Raje.
A statement by Mahila and Youth Congress units said the poor turn-out for the demonstration showed "lack of support and credibility on the issue."
"Kamat has clearly stated that his comments did not degrade Irani and he had only questioned her educational qualifications to hold the important portfolio of HRD and made a passing reference to her working at McDonald's as a waitress which is as per Irani's own admission," it said.
"None of their prominent leaders will be able to move around Mumbai as the Mahila, youth and student wings of Congress across Mumbai will gherao them," it warned.
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Kamat was known for his high regard for women and had always supported (party president) Sonia Gandhi in her commitment to the women's cause, it said.
Kamat, while referring to Irani's stint at McDonald's, had also asserted that there was nothing wrong with it, but this part was suppressed by the BJP, it alleged.
It also expressed surprise over suo motu notice issued to Kamat by National Commission for Women over the issue.