Co-operative-based sugar factory issues were discussed. Officials said Shah assured the delegation that steps would be taken.
The meeting is part of the exercise initiated by the home minister to meet the top police brass once in six months.
The National Disaster Response Force has deployed 11 teams for search, rescue and relief operations in the state where the death toll from heavy rains and landslide rose to eight on October 17.
Shah's comments came against the backdrop of a massive row over Rajnath Singh's recent remark that V D Savarkar had filed mercy petitions before the British at the advice of Mahatma Gandhi.
Members of farmers' body detained in Lucknow for trying to burn effigies of PM Narendra Modi, Amit Shah
The Socialist Kisan Sabha is a constituent of the Samyukt Kisan Morcha (SKM), an umbrella body of over 40 farmer unions that is spearheading the stir against the Centre's three agri laws.
Shah was in Goa to oversee BJP’s preparations for next year’s Assembly polls.
The remarks came after Shah talked tough on Pakistan and said the surgical strikes carried out by India five years ago sent a strong message to the world that no one can interfere with its borders.
He said under the BJP-led NDA rule, India gives a befitting reply to terrorist attacks which was not the case when the Congress-headed UPA was in power.
He said the "double engine" of BJP governments - in Goa and at the Centre - would help in the development of the state.
After the meeting which lasted for about two hours, the home ministry announced that the second round of talks will be held in November after the Diwali celebrations.
Incidentally, J&K has seen a worrying rise in incidents of violence, including a spate of civilian killings as well as that of security forces, over the past few days.
Responding to a question that opposition and critics term Modi an autocratic leader who takes all decisions on his own, Shah described the prime minister as a "democratic leader".
The meeting came oin the wake of several states warning of a possible power crisis due to the shortage of coal supply to power plants, officials said.
The visit comes two days after Union Home Minister Amit Shah pulled up senior security and intelligence officials over the spate of civilian killings.