The Edinburgh Solicitors Property Centre (ESPC) said 300 more homes were brought to the market last month than had been expected. And it warned that the increase in supply will lead to prices rising much more slowly.
The comments came after new figures showed that the average house price in Edinburgh increased by 5.9 per cent in the first three months of the year, to 207,440.
The total number of sales increased by 9.9 per cent on a year ago, to 899.
Neil Harrison, marketing and performance manager at the ESPC, said: "Our projection for the year is that house prices will stay at similar levels, with a couple of per cent growth in one quarter then possibly a couple of per cent drop the next.
"Over the year, we expect it to be pretty stable. There were 300 more houses brought to the market in March than expected so the supply side is improving and that will restrict price growth. There has been the usual group of people who have to move because of changes in their lifestyle but last year there was also a very low number of properties coming on and there is an element of pent-up supply from people who would have moved last year."
Within a selected sample of areas of Edinburgh analysed by the ESPC, the biggest price increases in the first quarter were seen in small flats in the Marchmont/Bruntsfield, where the average price was up 16 per cent on last year, at 258,106.
Smaller increases of around five per cent were recorded for similar properties in Stockbridge/Comely Bank and Gorgie/Dalry. There was also a significant 11.7 per cent decline in the average price of a four-bedroom detached house in Edinburgh's suburbs.
The average price of homes in East Lothian was higher than Edinburgh in the first quarter of the year.
A number of sales of larger properties in East Lothian helped its average price rise by 16.7 per cent to 210,592.
In West Lothian, prices increased by 5.1 per cent to 163,355, while Midlothian prices fell by 1.2 per cent to 161,618.
David Marshall, business analyst with the ESPC, said: "It goes without saying that activity is still some way below levels witnessed at the peak of the market in early 2007 and there's certainly no suggestion that things have returned to where they were prior to the credit crunch. Recovery is still likely to take some time."