Kolkata/IBNS: West Bengal Chief Minister Mamata Banerjee on Wednesday lashed out at the Central Bureau of Investigation for no tangible action in the rape and murder of 31-year-old trainee doctor at Kolkata's major state-run RG Kar Medical College and Hospital.

"CBI has been probing the incident for about 17 days. Why has no action been taken? We demand justice," Mamata thundered while addressing her party Trinamool Congress' rally in downtown Kolkata.

Mamata tried to mount pressure on CBI and the Centre on the same line in a counter to her administration facing public agony and Opposition's relentless criticism over the slow progress in the case until it was handed over to the premier central investigating agency.

"We wanted capital punishment through a fast-track court," the Chief Minister said, trying to ward-off the public wrath over the incident.

One person, a civic volunteer, has been arrested in connection with the case but protesting students as well as the victim's parents suspect more people are involved in the case.

Earlier this month, Mamata held a rally demanding justice for the victim triggering sharp responses from the Opposition and a memefest on social media.

Some social media users had taken a dig at her claiming that Mamata Banerjee was asking for her resignation from herself as she controls both home and health ministries.

Mamata accused the primary opposition Bharatiya Janata Party of diverting people's attention from the demand for justice in the RG Kar rape-murder case by calling a 12-hour state-wide bandh.

"The BJP called the bandh because they want to play politics over death. We want justice and capital punishment for the guilty. BJP wants to dilute the main aim for justice and defame Bengal," she said.

The 6 am-6pm bandh has been called by the BJP in protest against police's alleged assault on the students and protesters who marched to the state secretariat Nabanna.

The march was called by the students under the banner of 'Chhatra Samaj' demanding justice for the rape and murder and resignation of Mamata Banerjee.