The resolution was passed after three and a half hour discussion on the allegations made by Gen Singh recently.
Wrapping up the debate, 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.
The Chief Minister said if the Centre really wants to do justice with the institution of mainstream politics, it should not dismiss these allegations.
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"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.
"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.