The group - known as Basic - said the money must be available at once "as proof of their commitment" to address the global challenge.
The plea was issued after a meeting of the four nations in Delhi.
The funds were pledged in a non-binding deal agreed at last year's Copenhagen global climate conference.
The deal - the Copenhagen Accord - envisages that $30bn (£18.5bn) of aid will be delivered for developing nations over the next three years.
Basic members were instrumental in fashioning a political accord at the December climate summit.
The next round of negotiations is due to be held in December in Mexico.
After the Delhi talks, environmental ministers from the four nations issued a joint statement calling for rapid distribution of $10bn that industrialised nations promised to the developing world to tackle climate change in 2010. Read more.