"If you can't improve the law and order situation in Mumbai, you must resign," BJP state unit president Devendra Fadnavis said.
"Mumbai is no longer a safe city it used to be but has become rape city," the BJP leader said.
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Shiv Sena leader Neelam Gorhe said the government had failed to maintain law and order in the state.
NCP leader Vidya Chavan said the culprits should be nabbed and given stringent punishment.
Meanwhile, Patil who visited the Jaslok hospital where the woman is undergoing treatment, expressed confidence that the culprits would be nabbed soon.
"We have taken the incident very seriously. No one will be allowed to spoil the law and order situation," he said.
The government accords top priority for ensuring that women are safe, he added.