Its latest monthly survey, for November, suggests that prices have risen for the fourth month in a row.
The number of surveyors reporting price rises outstripped those reporting falls, with a positive balance of 35%.
Rics said this was the strongest reading since November 2006 and said the trend was likely to continue.
"For the fourth month in a row, the survey points towards prices rising, even though the general state of the economy would suggest that the housing market should not be faring as well as it is," said Rics spokesman Ian Perry.
"Despite modest increases in the number of properties coming on to the market, it is clear that this is not significant enough to keep pace with the levels of demand.
"Buyer enquiries are continuing to grow and with the pace of job losses now easing, the risk is that the new year could see a further wave of interest in the market," he added.
Rics carries out its assessment of the state of the market by asking its members a series of questions about prices, supply and demand.
It still indicative of an increasing level of buyer interest in the market .
Royal Institution of Chartered Surveyors New instructions to sell have risen for six consecutive months, but they have been outstripped by extra enquiries from potential new buyers.
The proportion of surveyors reporting an increase in new sellers instructions outweighed those reporting a fall, by 18%.
But the balance in favour of those reporting more enquiries from potential new buyers was much stronger at 28%, although this was down a bit from the 30% balance recorded the previous month in October.
"It is still indicative of an increasing level of buyer interest in the market," Rics said.
"The implication of the latest set of results is that fresh supply of stock is continuing to lag behind the increase in demand.
This provides further evidence that most housing market activity indicators continue to improve, albeit at a more modest pace than in previous months," Rics added.
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