While BSP chief Mayawati made a fresh demand for imposition of the Central rule, BJP Mahila Morcha demanded resignation of Yadav on "moral grounds for failing to check" incidents of atrocities against women.
Their demand made at separate press conferences here came a day after the woman died after policemen allegedly set her ablaze at a police station in Barabanki.
Accusing the UP government of downplaying the incident, Mayawati demanded the government's dismissal over its "failure" to control law and order in the state.
She said the manner in which the woman, whose son is a journalist, was allegedly torched at a police station in Barabanki was shameful for the government.
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Mayawati said even when the woman gave a statement, the CM was trying to downplay the incident by ordering a magisterial inquiry.
"He should have terminated the accused policemen and sent them to jail," she said.
The former chief minister alleged that the SP government was protecting a particular caste. Hours later, national president of BJP Mahila Morcha Vijaya Rahetker demanded resignation of the CM on moral grounds.