The elevated vacancy rates across the two biggest rental markets in Australia continued to weigh down asking rents, according to the latest figures from SQM Research.

Sydney and Melbourne were the only capital cities to report a decline in weekly asking rents in the week ending 12 December. In Sydney, rents were lower by 6.7% for houses and by 9.6% for units. Melbourne reported rent drops of 4.1% for houses and 6.7% for units.

Vacancy rates in the city remained elevated, with Sydney reporting a slight decrease to 3.5% while Melbourne maintained its 4.4% rate.

Louis Christopher, managing director of SQM Research, said that while rents continue to fall, there are signs that could point to a reversal in the abundance of listings in the CBDs of the two cities.

"They are still very elevated. But we could be starting to see some of the population moving back to the CBD and inner-city locations," he said.

Overall, national vacancy rates remained stable at 2.1%. Brisbane is the only other capital city, aside from Brisbane, to report a movement in vacancy rate, down from 2% in October to 1.8% in November.

In terms of asking rents, the decline in Sydney and Melbourne dragged the capital city average, with housing rents dropping by 1.8% and unit rents declining by 6%.

On the other hand, national asking rents increased for both segments, up by 7.8% for houses and 4.7% for units.

The tables below show the vacancy rates and the weekly asking rents in each capital city: