Mrs Beckett proposed the debate
British Foreign Secretary Margaret Beckett justified the debate by linking the issue to security.
But Russia and China said that as an international security watchdog, the 15-member council was not the right forum to debate climate change.
Mrs Beckett said an unstable climate could lead to increased world conflict.
The debate was initiated by the UK, which holds the presidency of the Security Council this month.
No resolution or statement arose from the discussion, in which 55 member states spoke.
Two world wars
"Our responsibility in this council is to maintain international peace and security, including the prevention of conflict," said Mrs Beckett.
She said the Stern report on climate change, which was commissioned by the UK government, warned of potential economic disruption on the scale of the two world wars and the Great Depression.
But China's deputy UN ambassador, Liu Zhenmin, said that the council lacked "professional competence in handling climate change".
Pakistan's UN delegate Farukh Amil said it was "inappropriate" for the Security Council to debate climate change.
He said there were other UN bodies which were better suited to dealing with the issue.
However, Panama, Peru and a number of small island states backed the British initiative.
Maritime dispute risk
UN chief Ban Ki-moon said that "issues of energy an climate change have implications for peace and security".
As examples, he said that scarce resources such as water and food could help turn peaceful competition into violence while migrations driven by climate change could deepen tensions and conflict.
The British mission to the UN circulated a paper explaining why it feels a discussion is needed.
It warns of "major changes to the world's physical landmass during this century", which will cause border and maritime disputes.
Some 200m people could be displaced by the middle of the century and "substantial parts of the world risk being left uninhabitable by rising sea levels".And there could be conflicts over "scarce energy resources, security of supply and the role energy resources play once conflict has broken out", the document adds.