The National Association of Estate Agents (NAEA) said the number of properties available to buy on estate agents' books decreased across the UK to an average of 39 per branch in March, from 44 in February.
March's average figure was the lowest the NAEA has seen for that month since its records started in autumn 2002.
Estate agents had an average of 397 prospective buyers on their books last month - around 10 times the average number of properties they had available.
The average number of sales agreed decreased in March, to around 10 per branch. In February, 11 sales were agreed per branch, the highest number recorded since September 2007.
One in four (25%) sales agreed in March involved first-time buyers, up from 22% in February.
Nearly two-thirds (64%) of estate agents said they have seen demand for properties from buy-to-let investors decrease since a stamp duty increase was introduced for this sector on April 1 2016.
Mark Hayward, chief executive of NAEA Propertymark, said: "There are currently 10 house hunters chasing each available property, and with supply at the lowest level for March since records began, building more homes to satisfy demand needs to be a priority."
A separate report from the National House Building Council (NHBC) has found the number of new-build homes being registered at the start of 2017 was the highest in a decade.
Some 42,470 new homes were registered in the first quarter of 2017, showing the strongest quarter since the third quarter of 2007 according to the NHBC, whose figures represent homes to be built in the months ahead.