Some small banks have begun to pass on the central bank's June rate cut, but home owners are still waiting for the big four to make a move.
Beirut Hellenic Bank became the first lender to cut its interest rates by 25 basis points on Wednesday, 24 hours after the Reserve Bank cut the cash rate by the same margin.
The multicultural bank formerly known as Laiki Bank Australia has been operating since 2011, and has 16 branches in Sydney, Melbourne and Adelaide.
Chief executive James Wakim said the cut came despite the fact smaller banks have particularly high funding costs.
"The bank has been working hard over the last several months to reduce its funding and operating costs and we are very pleased to advise we are now in the position to pass the full 25 point RBA rate reduction on to our home loan customers, and to be one of the first Australian banks to do so," Mr Wakim said.
Bank of Queensland is the largest bank to have cut so far, reducing its standard variable rates by 20 basis points on Tuesday.
Commonwealth Bank, Australia's largest home lender, plus National Australia Bank and Westpac on Wednesday said their interest rates remain under review.
ANZ will hold its monthly rates meeting on Friday.
The pressure is mounting on the big four to cut their rates by 25 basis points, with the calls led by Treasurer Wayne Swan and Prime Minister Julia Gillard.
But the Australian Bankers' Association said funding costs for the major banks were at their highest levels since the global financial crisis.
Mr Swan acknowledged there was vulnerability with offshore funding but said strong competition for deposits was not a good enough excuse to hold back on the latest rate cut.
"Of course they would argue that the cost of their domestic deposits has gone up ... I just don't believe it is justified," he told Network Ten.
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