The resolution was passed at the end of three and a half hour discussion on the allegations made by Gen Singh recently.
While concluding the discussion, Chief Minister Omar Abdullah proposed the one-line resolution for a thorough probe which was unanimously adopted by the house.
Omar said the mainstream political institutions were in danger and the allegations levelled by Gen (retd) Singh had caused unprecedented damage to these institutions.
"We are not responsible for this damage. It was your (Centre's) inquiry (into the functioning of Technical Services Division of Army). The leak took place from there (Delhi) but we are bearing the consequences," Omar said.
The Chief Minister said if the Centre really wants to do justice with the institution of mainstream politics, it should not dismiss these allegations.
"Right or wrong, we will wait for the outcome of the inquiry. We don't want to jump to the conclusion but there should be a time-bound probe that will bring out the facts. There is no other way to restore the image of mainstream politicians among the people," he said.
Omar said the politicians of the state have to face the people of the state few months later in Lok Sabha elections and state Assembly polls.
"If we have to face the people with this stigma of V K Singh, then that might be the Centre's wish. As much as we would try to give explanations who will buy them," he said.