SYDNEY (Reuters) -Australia's housing shortage is creating challenges for first-time homeowners and migrants but will continue to push prices higher, CEOs of two of the country's biggest banks said on Tuesday.

The heads of No. 2 lender National Australia Bank and No. 3 rival Westpac Banking Corp said the country needed to speed up approvals to boost the rate of housing construction as the country grapples with surging migration and shrinking home affordability.

"I'm positive on the housing market," said Westpac CEO Peter King at the AFR Banking Summit in Sydney, citing "the fundamentals of 'we need more houses developed'."

"When you have a supply-constrained market that means the price will probably go up," he said.

"From a societal perspective, it's too expensive," King added.

NAB CEO Ross McEwan told the event the country needed migrants to fill skills shortages across the economy, but "we've got to get the impediments out and get the tradies (tradespeople) in and get building".