He also appealed the thousands of protesters on the capital's streets, demanding justice for the victim, to withdraw.
"A probe will be conducted to look into the incident and suggest measures to check such crimes in Delhi...the Criminal Procedure Code will be amended to enhance punishment in such rarest of rare cases," Shinde told reporters at a hurriedly-convened press conference.
"I appeal all the protesters to withdraw as you have shown solidarity in the issue," he said adding: "The government shares the concern expressed by the society."
Making an emotional statement, Shinde said he had three daughters and was equally concerned about safety and security of women.
"The government is serious on the issue.. we are committed to safety of women," he said.
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Shinde ruled out the demand made by Leader of Opposition in Lok Sabha Sushma Swaraj that a special parliament session be convened to make the law against rape more stringent.
"There is no need for a special session," he said.
He also said policemen who have been found responsible for dereliction of duty in the gang rape incident will be suspended, and announced a slew of steps to ensure women were better protected in the city.
"More public transport will be available at night and GPS system will be fitted on buses to track them easily...all personnel of the buses will have to carry identity cards...and there will be enhanced patrolling by police on city roads leading to entertainment hubs," Shinde said.
The home minister said there was sufficient evidence against the six accused and police would soon file a charge sheet against them.
"We are requesting for a speedy trial on day to day basis," he said.
The home minister also said that permit of all nine buses owned by the transporter who owned the bus in which the crime was committed have been cancelled.
He assured best medical care for the victim and that the government will do whatever is needed in the matter.