"The rape and murder indicate that the Kerala government was trying to cover up the incident as it took days to register
the case," Singh, who is on a two-day visit to the state for campaigning in the May 16 assembly polls, said.
Addressing a series of election rallies in the state, Singh said there should be a CBI probe into the case.
The shocking case is being described as "Kerala's Nirbhaya" for the chilling similarity to the Delhi rape case of 2012.
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"CBI probe should be held into the murder. As this country's Home Minister, I assure you that as soon as we get a recommendation (in this regard) from the state government, we are prepared to conduct CBI probe," the minister said at Chathanoor in Kollam district.
"I assure you that the guilty shall be punished," he said.
The Dalit woman, who hailed from a poor family, was allegedly subjected to rape and brutal assault using sharp edged weapons before being murdered at her house at nearby Perumbavoor in Ernakulam district on April 28.
The incident had its echo in Parliament with members demanding "exemplary punishment" for the culprits, besides triggering widespread protests across the state.
Singh also flayed CPI(M) veteran V S Achutanandan for not disclosing the name of the VIP in the sensational Killiroor and Kaviyoor sex scandals as "assured" by him and said his credibility in Kerala politics had come to an end as he failed to keep his promise.
There were allegations that some influential persons were involved in the two cases.
At another meeting, Singh said, "UDF and LDF have treated the people of the state like a football, kicking them around for political gains".