Chidambaram, who is on a two-day visit to the state, said the Army has the responsibility for "conventional" defence at the borders and also countering infiltration and terrorism.
Political parties in the state have been demanding the repeal of AFSPA on the ground that it gave unfettered powers to the security forces, whom they accuse of "high-handedness".
Chidambaram said the issue of AFSPA was flagged two months ago during a meeting with Chief Minister Omar Abdullah and the two leaders had agreed to look in to the matter after the elections.
"I promise to look at the matter. I have to discuss it with the Defence Minister and the Prime Minister ... it will be looked into in all earnestness," he said adding "government will take into account every essential aspect".
The Home Minister said that maintenance of law and order in inhabited areas was the "primary responsibility" of the state government and the Army would chip in if its help was sought.
He said government has the intention to redraw responsibilities though the process would take some time.
Chidambaram said stability has been reasonably assured after the elections to the state assembly and the Lok Sabha.
The militant activity has been contained and reduced, he said adding that he had assured the Chief Minister that Centre will extend aid in every possible manner to improve the security in the state.
However, he said agitational activities were on the rise and come in the way of development works and affect normal life.
"I appeal to everyone that agitational activities must be contained so that they do not interfere in the normal life of the people.
"I believe most organisations have begun a rethink on this subject. I welcome the rethink so that it does not come in the normal life of the common man and normal governance," Chidambaram told reporters here.
Asked about the Shopian incident in which two women were allegedly raped and murdered, Chidambaram said Abdullah had briefed him on the matter and it was the intention of the state government to hold a thorough inquiry and punish anyone found guilty.
