NSW Premier Gladys Berejiklian has defied pressure from Prime Minister Malcolm Turnbull to embrace controversial gas exploration, saying her state is "not budging" on the politically charged issue.

Speaking after a Council of Australian Government meeting in Canberra on Thursday, the Prime Minister stepped up pressure on his Coalition counterpart to approve the much-disputed $3.6 billion Narrabri Gas Project project by energy giant Santos, saying it would go a long way to helping meet a predicted east coast gas shortfall.

"[The project] is currently going through the planning process. What we would look forward to is that planning process being completed," Mr Turnbull said.

"The extra ... 58 petajoules [of gas produced per year] would make a very significant difference in supply and ... price is a function of supply and demand."