In the three months to January, a net balance of +13% surveyors reported increases in rental values, down from +21% in the previous quarter.
Demand for rented accommodation remained relatively strong with 19% more surveyors reporting rises rather than falls in interest from prospective tenants.
They however noted an increasing number of first-time buyers looking to beat the end of the stamp duty holiday in March and therefore slowing the pace of rental growth.
Housing supply to the market has remained positive for four consecutive quarters as surveyors said they saw a rise in new instructions.
Also around 4% of landlords chose to place their property on the sales market in the three months to January.
RICS says this was driven by an upturn in prospective property buyers and slowing rental growth.
Looking ahead, RICS said it expected growth in rental values to continue to slow.
Michael Newey, spokesman at RICS, said: “With many potential first-time buyers having been forced into rented accommodation due to problems with obtaining affordable mortgage finance, rental prices have grown quickly across much of the country in recent times.
“However it seems that tenants may be becoming less willing to meet increasing rental values.
“While still growing demand from potential tenants is also beginning to slow. With a recent upturn in buyers entering the sales market prior to the expiry of the stamp duty holiday in March, it seems that those who are in a position to get a foot on the property ladder may have chosen now to do so.”