"India has taken a position and we don't see any reason for changing our stand," said Krishna to journalists.
"We have taken a principled stand and and so the question of India revisiting it stand depends on a number of other developments that would address our concerns."
UN General Secretary Ban Ki Moon urged India and eight other countries to approve the agreement.
"The CTBT is a fundamental building block for a free world of nuclear weapons," said Moon.
"By establishing a global norm against testing, the CTBT has made a significant contribution to the world community's efforts to prevent the proliferation of nuclear weapons and to promote nuclear disarmament."
But Krishna reasoned that India was not in a position to sign the pact.
"India's stand remains unchanged. We have spelt out why we our unable to sign the pact as it is," he said.
In a meeting chaired by US President Barack Obama, the Security Council passed a nuclear non proliferation resolution.
It directs all states to "refrain from conducting a nuclear test explosion and to sign and ratify the Comprehensive Nuclear Test Ban Treaty (CTBT) to bring it into force early."