Chairmen of two of the country's biggest banks have sounded a warning over the future threat from global technology giants trying to muscle into Australia's highly profitable banking industry.

As banks try to fend off a mounting push for a high-powered inquiry, National Australia Bank chairman Ken Henry and Westpac chairman Lindsay Maxsted highlighted the pressure on banks' strategies from the likes of Google or Apple.

"The competitive challenge in our industry is not so much that one of us is going to cut the other's throat. It's not that. It's that we are going to be challenged beyond our ability to cope by the big IT platform providers, the Googles and the Apples and so on," Dr Henry said at a business lunch in Sydney.

He said the competitive threat – which he saw as emerging over roughly the next decade – was forcing NAB to ask itself what the technology giants may be able to offer customers, and how the bank could beat this by using new types of technology.