Shah was today accused of misusing his powers and police machinery for illegal surveillance of a young woman in 2009.
"If these claims are true, it is a very serious allegation and BJP will be forced to rethink their PM candidate," Law Minister Kapil Sibal told reporters.
"BJP accusing us of dirty tricks is expected, but this is what they did with Tehelka and Tarun Tejpal also. Why would a father want his daughter stalked? This issue has to be investigated," the senior Congress leader said.
However, the two websites also said "at this point of time, Gulail and Cobrapost have no means to independently verify these charges."
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Congress spokesman Meem Afzal, speaking separately, demanded a CBI inquiry into the allegations against Shah. He also wanted Shah, a close aide of Narendra Modi, to come clean on who the "saheb" for whom he had ordered the surveillance.
He also wanted to know why the snooping was being done, when it is illegal to follow any person in such a manner.
"The nation wants to know why the former minister of state for home of Gujarat who has been jailed in the Ishrat Jahan case and now is on bail had ordered the surveillance," he said.