The building society said that prices increased by 0.3% in July, the second month running there has been a rise.
Nationwide said the increase appeared to be at odds with recent signs of cooling in the housing market.
Over the last year, prices are up by 2.9%, slightly lower than last month’s rate of 3.1%.
Earlier this month, the Royal Institution of Chartered Surveyors (Rics) said estate agents had fewer properties on their books than at any time over the last 40 years.
“Constrained supply is likely to continue to provide support for house prices and, as a result, we continue to expect prices to rise by about 2% over 2017 as a whole,” said Robert Gardner, Nationwide’s chief economist.
However the ratings agency Moody’s said it thought that house prices were now likely to fall outright.
HM Revenue and Customs reported that the number of housing transactions dropped to its lowest level for eight months in June.
And earlier this week, the Bank of England said the number of mortgage approvals in the month fell to a nine-month low of 64,684.
Based on its own data, the average price of a house or flat in the UK is now £211,671, the Nationwide said.