Yorkshire Party councillor Andy Walker put forward the motion at a full council meeting of East Riding Council.
The issue is a hot topic coming days after investors in energy firm Rathlin Energy (UK) Ltd said the biggest gas and oil field in nearly 50 years may have been found at West Newton eight miles from Hull.
Coun Walker said: "This is about responsibility and leadership time is precious.
"The signs of global warming are clear, the emergency is real and racing towards us. We have less than 12 years to avoid the tipping point.
"We are part of the problem - with leadership we can be part of the solution."
The motion, which followed a protest involving around 70 demonstrators outside County Hall, called for the council to take steps including setting up a councillor working party to oversee an environmental audit and take practical steps to reduce emissions and the council's carbon footprint.
Quoting Sir David Attenborough he added: “If we don’t take action, the collapse of our civilisations and the extinction of much of the natural world is on the horizon.”
However an amendment was put forward by Tory councillor Chris Matthews, who said a scrutiny committee, was better placed than full council, to monitor "progress and update members on important and complex issues."
All the Conservatives voted for the amendment. Against were the Liberal Democrats, Yorkshire Party and Independents.
Lib Dem councillor David Nolan said it was a "wrecking" amendment, "a complete negation of the substance of the motion" in what was an issue of "massive public interest to residents."
Afterwards Richard Howarth from the Green Party said: "The collapse of society and our environment is imminent and the East Riding Council is in complete denial of the urgency of the situation."
Mike Brookes, a resident from Walkington, said the Conservatives were faced with a dilemna - supporting drilling for oil and gas - or declaring a climate emergency.
He added: "They have gone with fossil fuels basically."
Conservative councillor Mike Stathers later released a statement saying there was a "large gap between the outage generated by renewables and the national energy needs."
He said the West Newton site was close to a gas pipeline and Rathlin had permission for test drilling.
He said: "We can reassure residents that we will continue to closely monitor all activities at West Newton and should there be any breach of the licence or planning permissions we will not hesitate to take appropriate action.”