The Commonwealth Bank's chief executive Ian Narev has ruled out a rate cut independent of the Reserve Bank in the short-term.

The major banks have increased mortgage rates relative to the Reserve Bank's cash rate since the onset of the financial crisis, by lifting rates when the Reserve has kept them on hold, increasing them by more than the RBA's cash rate rises, or not passing on the same percentage point reduction as the RBA when official rates have fallen.

Westpac's chief executive Gail Kelly and Mr Narev had both intimated previously that their banks will eventually reduce their mortgage rates relative to the cash rate as funding costs ease.

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However, speaking to AM, Mr Narev says funding costs remain high, meaning that a potential home loan rate reduction relative to the Reserve Bank's cash rate will have to wait.

"You've got to bear in mind that what puts pressure on our wholesale funding is the cost of new funding relative to the cost of the funding it replaced, which isn't usually funding from a month ago, it's funding from two or three years ago, and that continues to go up," he said.

"The other factor we've got here is that deposit competition is increasing and, as I said before, depositors do well, but that does continue to put pressure on our deposit pricing so, as we sit today, unfortunately we're not at the end of a cycle where funding costs are going up."

Ian Narev says that situation is unlikely to change in the short-term while volatility and uncertainty about Europe's economic future reigns.

"We think there must be a solution, it involves greater integration, but we can't see how that solution's going to be workable politically and I continue to hold that view today. And I don't think that uncertainty's a good thing for the global economy or indeed the economy here in Australia," he observed.

"So, we don't foresee a big disaster in Europe, although that is a possibility, but at the same time we can't really see yet what the catalyst is going to be for a significant improvement."

However, despite the prospect of mortgage rates remaining high relative to the cash rate and the bank's record $7.1 billion profit, CBA's chief has brushed aside calls for a another banking enquiry.

"We do think it's a very competitive banking system, so I don't think you need an enquiry to tell as that. And indeed we've had various versions of enquiries trying to get at that and, I think what I've said before on the impact on margin shows that it is competitive," he added.

"But there are legitimate questions about Australia's long-term funding that need public debate and, if the way to do that is through an enquiry, then we would be happy to participate in that."

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