Non-major lenders amp up the pressure on Australia's big four banks as they pass on the full benefit of the Reserve Bank's 0.25 per cent official rate cut to their customers.

Leading second-tier banks like the Bank of Sydney and Bank Australia revealed that they would deliver the full cut on their standard variable mortgages. Bank Australia lowered its standard variable rate from 4.99 per cent to 4.74 per cent—0.5 per cent cheaper than the average base mortgage rates of the four major banks at 5.22 per cent. Bank Sydney will also lower its variable mortgage rate to 3.63 per cent from 3.88 per cent.

Aside from lowering the home loan interest rates, Bank Australia is also planning to pass the full rate cut to all its credit card holders and personal loan customers. Its low-rate Visa card will be lowered to 9.39 per cent, making it one of the cheapest in the Australian market.

Meanwhile, Prime Minister Malcolm Turnbull asked the country's biggest banks to justify why they only passed part of the official rate reduction, arguing that the banks should be made fully accountable for their decisions.

"The commercial banks should pass on the full rate cut—they should pass it all on. They should do that, and if they are not prepared to do it, then their chief executives should explain very clearly to the Australian people and their customers why they have not done so," he said. "They operate with a very substantial social licence, and they owe it to the Australian people and their customers to explain fully and comprehensively why they have not passed on the full rate cut—and they must do so."