India has rejected Pakistan’s proposal for a United Nations (UN) probe into the chain of killings along the Line of Control (LoC) that began on Sunday morning and led to the killing of two Indian soldiers on Tuesday.

The Indian response was to a Pakistani suggestion for investigating the incidents by the UN Military Observer Group in India and Pakistan (UNMOGIP) which is present on both sides of the LoC.

But high-level sources said the brutality with which the Indian soldiers were killed on Tuesday will be taken up with Pakistan through back channels. “If you stand up and start shouting, Pakistan Army will never agree. There are other ways of approaching them on the issue,” they said.

The Indian Government’s reaction came before news came of a Pakistani soldier being killed on Thursday but sources said the stand remained unchanged.

“We are certainly not going to agree to internationalise the issue or allow the UN to hold an inquiry. That demand is obviously rejected out of hand,” Union Finance Minister P. Chidambaram said at a news conference after taking part in meetings of the Union Cabinet and the Cabinet Committee on Security which was briefed by Defence Minister A. K. Antony.

“We take a serious view of what happened. Whatever has to be done will be done,’’ added Mr. Chidambaram while describing the decapitation of an Indian soldier as brutal.

At another news conference, National Security Advisor Shiv Shankar Menon said there had been an increase in ceasefire violations and infiltration attempts. “In 2012 there was an increase overall over 2011. That is a fact. And that is something we are dealing with, both ourselves and with the Pakistani authorities,’’ he said.

Mr. Menon referred to Foreign Minister Salman Khurshid’s statement and said “he has made it quite clear that he is not jumping to any conclusions at this moment. So, I suggest you wait.”

Asked about the beheading of an Indian soldier, Mr. Menon said, “[the] Government has said what it has to say on the event. You have a selection of adjectives — reprehensible, barbaric, dastardly, whatever you want. Sadly, it is not the first time this has happened. I hope it never happens again. But we have also told you exactly what we intend to do. So, now I think you should let Government go about its business.”

Both India and Pakistan have denied the involvement of their troops. India has said its troops indulged in “controlled retaliatory fire” early on Sunday morning and denies Islamabad’s allegation that Indian troops crossed the LoC to kill a soldier and seriously injure another.

Similarly Pakistan denied any hand in Tuesday’s incident in which two Indian soldiers were killed whereas New Delhi says Pakistani troops crossed the LoC and utilised the poor visibility due to dense fog to ambush a patrolling party.

Separately, the army clarified in reference to The Hindu story ‘Runaway grandmother sparked savage skirmish on LoC’ that Maj. Gen. Khandare and not Maj. Gen. G.S. Rawat is currently the General Officer Commanding of 19 Infantry Division. The army also denied that any permission was ever sought by the GOC for aggressive action against any Pakistani post.