"Mortgage rates for owner occupiers are already around the lowest level since the 1960s and lenders are generally expected to pass on most, if not all, of the cash rate cut to mortgage interest rates", said Lawless.
The Reserve Bank earlier ended a almost three-year pause in policy adjustments when it eased the cash rate to 1.25%.
The cut was the first since 2016 when the bank cut rates twice in May and August.
"Escalating trade tensions are contributing to growing uncertainty in the global economic outlook and the impact of flood and drought and fires and a softening housing market have weighed on the economic outlook here at home", he said, adding that is why Parliament should pass the government's tax cut plan in full when it heads back to work in July and support the work underway on infrastructure and skills.
"It will assist with faster progress in reducing unemployment and achieve more assured progress towards the inflation target".
The Reserve Bank is widely expected to drop the rate to 1.25 per cent on Tuesday, in an effort to lift employment conditions and preserve its inflation target.
"Much will depend on how the evidence evolves, especially on the labour market", Mr Lowe said in a dinner speech to the business community on Tuesday night.
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Mr Frydenberg has also reminded the banks of the recent findings of the banking royal commission, to underline his argument.
Prior to Tuesday, just half the 12 RBA cuts since November 2011 were passed on in full - or within 0.01 percentage points of full - by the major banks.
Shadow treasurer Jim Chalmers argues the rate cut must be passed on to fulfill the central banks' goal of shoring up the economy.
"We know that people can move between banks and seek a better deal as well, and I'd encourage them to always look for the best possible deal for themselves and for their families and their businesses", he told Nine's Today program. "They've got no excuse for not doing that", he told ABC Radio Melbourne.
"The farmers who grow our food are struggling with drought and deserve the full rate cut to be passed through", he said.
Canstar reports there were 531 interest rate moves in May, with 85% (449) of these being cuts to fixed rates.
"We can only hope that if the banks pass on this official cash rate cut, in combination with the potential for loosened mortgage rules flagged last month, we will see more positive movement in terms of demand for property as consumer confidence is bolstered".