The index also showed that the annual rate of price inflation remained relatively high at 9.0%.
Commenting on the figures Martin Gahbauer, Nationwide's chief economist, said: “The price of a typical UK property rose by a seasonally adjusted 0.7% month-on-month (m/m) in March, largely reversing the 0.8% m/m fall measured in February. The smoother three month on three month rate of inflation edged down further from 1.8% in February to 1.6% in March. At £164,519, the average price of a typical property is 9.0% higher than a year earlier.
“The last two months are consistent with a relatively flat profile for house prices, and in line with the recent drops seen in buyer enquiries and house sales. Preliminary figures show that the number of loans taken out for house purchases failed to recover from January’s large dip, suggesting that weakness in house sales at the start of the year may have been due to more than just the snowy weather. With greater than usual political and economic uncertainty ahead of the upcoming general election, potential homebuyers are proceeding cautiously.
“At the same time, the number of homes for sale has not increased appreciably, meaning that the impact of lower buyer activity on house prices has not been too negative. If this trend continues, we are likely to see relatively few properties changing hands, but with prices fairly stable.”
Simon Rubinsohn, RICS chief economist, added: "The rise in house prices in March according to data released by the Nationwide Building Society today should not come as a surprise.
"Although more supply has begun to come on to the market, it has yet to reach the level where it is matching demand.
"Significantly the latest RICS Housing Market Survey still shows more agents seeing prices rather than prices declines.
"Meanwhile, the stamp duty announcement in the budget should provide a further boost for demand.
"As a result, we continue to believe that house prices will remain firm through much of the remainder of this year.
"From a regional perspective, the Nationwide numbers predictably show London and the South continuing to see the strongest price performance.
"This is a trend that is set to persist over the coming months according to RICS surveyors. It is also something that is broadly consistent with the nature of the economic recovery now unfolding."