Menon, who was deputed by Prime Minister Manmohan Singh as part of efforts to keep other parties in the loop, told the BJP leaders about the government's moves in the wake of the gruesome incident.
He is understood to have referred to the remarks of Swaraj, Leader of Opposition in the Lok Sabha, that "If Pakistan does not return the head of martyred soldier Hemraj, India should get at least ten heads from the other side."
She made the comments in Mathura yesterday after meeting the family members of Lance Naik Hemraj, who was beheaded and his head taken away by Pakistani soldiers after a cross-LoC attack in Mendhar area of Jammu and Kashmir on January 8.
Swaraj explained to Menon, who drove to her residence, that she had made the comments in the backdrop of inconsolable pain and anger in the family of Hemraj.
The NSA, who is understood to be keeping leaders of other main parties too in the loop, also referred to the remarks of BJP President Nitin Gadkari that India should move the United Nations on the gruesome killing.
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Menon explained that the government was against such a step as it would internationalise the issue.
To this, Jaitley, Leader of Opposition in the Rajya Sabha, is understood to have told Menon that this was not the party's position and Gadkari's comments might have been misunderstood.
The NSA told the BJP leaders that the government would keep the Opposition in the loop over any situation arising out of the incident as it wanted both sides to be on the same page.
The Prime Minister had yesterday talked to both Swaraj and Jaitley on the LoC situation to assure them that Opposition will be taken into confidence on whatever steps are taken.