Perth is the only mainland state capital to have recorded a rise in housing prices last week, as the national average has edged lower.

Prices were up 0.2 per cent in Perth, but steady in Sydney, down 0.5 per cent in Melbourne, and down 0.3 per cent in both Brisbane and Adelaide.

The five-city average price was down 0.2 per cent, slowing the annual growth rate to 6.7 per cent, from 7.0 per cent a week earlier and 10.3 per cent this time last year.

Sydney has held its place at the top of the list of annual rises with a gain of 9.7 per cent, although Melbourne is not far behind at 8.3 per cent.

Annual rises were more subdued in Brisbane (3.7 per cent) and Adelaide (3.3 per cent), while Perth has continued to wilt amid the mining investment downturn, with a 5.4 per cent fall.

Led by Sydney’s 83.3 per cent of auctions ending with a sale, the average auction clearance rate last week rose to 77.9 per cent.

That was the highest since May last year and well up from the 67.4 per cent clearance rate in the corresponding week of 2015.

“The clearance rate has remained above 70 per cent since the last week in July,” CoreLogic said in its weekly report.

However, the higher clearance rate was achieved on only 2,405 auctions, down by 16 per cent from 2,858 the same time last year, the figures from CoreLogic also show.

Despite the higher clearance rate, the lower auction numbers imply a slightly lower number of completed sales at auction last week compared with a year earlier.