The Nationwide said the rise was helped by the government's Funding for Lending Scheme, designed to bring down the cost of credit, and improving job prospects.
The annual rate of price growth rose to 1.9%, the fastest pace since September 2010. The increases means that the average house now costs £168,941.
But Nationwide said there were few signs the housing supply was improving.
Robert Gardner, Nationwide's chief economist, 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."
The Funding for Lending Scheme allows banks to borrow money at a discount from the Bank of England, providing they can show they have passed it on to customers in the form of loans.
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.
London was the top performer, with prices up 5.2% in the second quarter year-on-year. Prices are now 5% above their 2007 peak of £318,214, said Nationwide.
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.
Meanwhile, Nationwide said that the supply of housing remained sluggish, 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, Nationwide said.
