The BJP said the matter involving the woman in Gujarat should be put to rest after her father did not want any probe.
Countering the Congress demand for a central probe, the BJP said it was "politically motivated" and wondered why it was insisting on this when the matter was a state subject.
Shah, the man at the centre of the controversy, refused any comment when he was repeatedly asked about his stand in Agra where he is overseeing arrangements for a Modi rally to be held later in the week.
"Yes, I always said that," Union Minister and senior Congress leader Kapil Sibal said when asked whether the BJP should replace Modi as the party's PM candidate in the aftermath of the snooping controversy. "Sooner or later it will be done," he added.
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Senior BJP leader Arun Jaitley said there is more political interest in the subject, rather than facts.
"Even after the concerned woman and her father are saying that security was provided on their request they are not complaining, but Congress is concerned about this," the Leader of Opposition in the Rajya Sabha said.
"The basis of the case is in itself wrong. Security and protection is not snooping," he added.
Questioning the motive of Congress, Jaitley said, "Has this (Congress) government ordered a probe how thing were done in other cases? When the woman and her father herself was saying that this was the protection given to her at her own request for some specified reasons, then where is the question of probe in this."
BJP spokesperson Prakash Javadekar said Congress should let the matter rest now that the girl's father has written to the National Commission for Women stating that the Modi government had made security arrangements for his daughter with the family's consent.
The father has also told the NCW in a letter that his daughter does not want any probe into the issue as there was no encroachment on her privacy.
Notwithstanding the letter, the NCW asked the Gujarat Government to probe the incident.