The annual rate of price growth rose to 1.9%, the fastest pace since September 2010, and the average house now costs £168,941.
Robert Gardner, chief economist at Nationwide, said: "Demand for homes has been supported by further modest gains in employment, as well as an improvement in the availability and a reduction in the cost of credit, partly as a result of policy measures, such as the Funding for Lending Scheme.
"Signs of a modest improvement in wider economic conditions may also be playing a role in boosting buyer sentiment."
House prices in the second quarter of 2013, compared with the previous three months, were 0.4% higher, and up 1.4% compared with the same period a year ago.
On a regional basis London recorded the largest growth with a 5.2% year-on-year price increase during the second quarter.
However annual price growth in Wales and Scotland continued to decline. Northern Ireland was the worst performer, with prices down 2.1% in the quarter from a year earlier.
Brian Murphy, head of lending at Mortgage Advice Bureau, said: “Homeowners will be delighted to see a third month of house price increases in Nationwide’s figures.
“Potential buyers will be comforted by the fact that mortgage rates are still heading in the opposite direction.
“As property becomes more desirable by the week, falling fixed rates mean they can still enjoy exceptionally low interest on their loans for increasingly long periods of time.
“This golden age of rate reductions is coaxing more borrowers through the door, and with the guidance of specialist brokers there are plenty of favourable deals to help them contend with rising prices – especially as lenders are playing their part with some offering low product fees.”
Murphy said the onus is now on the government to agree the finer details of its mortgage guarantee scheme as quickly as possible.
He said: “Its £3.3bn commitment to social housing was a small victory in this week’s Spending Review, but a meagre share of the total £100bn investment.
“We must hope it encourages the private sector to put more faith in property and act now to increase housing supply.”
Nationwide said that the supply of housing remained slow with data showing a further decline in building activity.
In the first quarter of 2013 housing completions in England were down 8% on the same three months in 2012, and are 40% below 2007 levels.
