In a statement here, Achuthanandan wanted the Centre and the Congress's national leadership including Defence Minister A K Antony to make their stand clear on the matter.
The Marxist leader said as per IPC, authorities were bound to register a case when a woman dies under "unnatural circumstances" within seven years of her marriage.
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When Sunanda died in a hotel in Delhi, certain quarters, including the hotel employees, had said it appeared to be a death under "unnatural circumstances".
He said the people of Kerala were keen to know the position of Antony on the issue.
Tharoor, who won Thiruvananthapuram Lok Sabha seat in 2009, is back in the fray to defend the seat.