Overall, only 9 per cent more surveyors in England, Wales and Scotland reported seeing price falls compared with those who reported rises, well down on a figure of 21 per cent more during September.
The group said with sales rising and the number of new properties coming on to the market remaining static, the average number of unsold properties surveyors had on their books fell slightly to 74.
It said it remained a buyers' market, but the balance of power wasbeginning to shift as the recovery continued.
RICS spokesman Jeremy Leaf said: 'This month has seen further evidence of a pick up in the market with the recovery in would-be buyer interest.
'Contributing factors include diminishing uncertainties over the future of interest rates and rising employment which is lifting the demand for homes.
'The return to more balanced market conditions is welcome, though negotiations between buyers and sellers remain hard, and over-priced property continues to remain unsold. A return to boom conditions is not at all evident.'
Surveyors were positive about the outlook for the market going forward, expecting modest price increases in most regions of the country over the coming three months.
In London prices increased during October for the first time in 18 months, while across the rest of southern England they either stabilised or showed marginal declines.
The cost of property continued to fall in northern England and the Midlands, although prices rose in the North West and Scotland.