Asked if there would be no new support measures until the budget, Mr Albanese said, "that's not necessarily the case at all".

He said cost of living measures were discussed by cabinet at its first meeting for the year on Monday.

"The government continues to work and will continue to look at whatever measures we can undertake," Mr Albanese told ABC radio.

As the government faces a fight to hang on to Victorian seat of Dunkley at a byelection following the death of sitting Labor member Peta Murphy, it is being forced to consider ways to relieve the financial strain on households without sparking a lift in inflation.

"We know that the cost of living pressures are there, and we know that the fight against inflation is not over," he said.

"We'll continue to look for targeted cost of living relief, how we can make a difference for people without adding to inflation."

One particular source of inflation is housing, particularly rents, and the government was keen on Monday to spruik the opening of its Housing Australia Future Fund.

Housing Minister Julie Collins announced that Housing Australia had launched the first round of tenders for social and affordable housing.

"This is the single biggest investment [in social and affordable housing] in more than a decade," Ms Collins said.

"We're talking 30,000 from the Housing Australia Future Fund in the first five years and further 10,000 from the National Housing Accord."

The minister said work would start in the first half of the year on homes provided for under the $2 billion social housing accelerator.

But the initiatives will do little to alleviate the housing costs currently being faced by households, particularly renters and those with a mortgage.

Property market analyst CoreLogic said that rents had grown faster than house values for the past two years and the Australia Bureau of Statistics reported that rents accelerated to an annual rate of 7.1 per cent in November, making them one of the big drivers of inflation.