Prices on the three month measure slipped back into negative territory following successive small gains in the two previous months.
Prices in the three months to June were 0.5% lower than in the same period a year earlier.
There has been a marked improvement in the annual rate over the past 12 months with an annual decline of 0.5% or less in each of the past three months. The annual rate stood at -4.2% in May 2011.
Martin Ellis, housing economist at Halifax, said: "The ending of the stamp duty holiday at the end of March appears to have distorted house price movements and sales in recent months. Nonetheless, despite falling back in April and May, sales remain slightly higher than a year ago.
"Continuing low levels of mortgage payments relative to income and recent increases in employment may have helped support house prices so far this year. We expect little change in prices and sales over the remainder of the year provided that the UK's economic outlook does not deteriorate significantly."
Ed Stansfield, chief property economist at Capital Economics, said the June monthly bounce does little to alter the underlying trend which shows that house prices are grinding lower, albeit only slowly.
And he added: “The latest Halifax index is clearly at odds with last week’s figures from the Nationwide, which showed that prices edged down by 0.6% in June.
“Of course, such month-by-month divergences are common and, viewed on a 3m/3m basis, the two indices now show a more similar picture.”
Over the past three months Halifax shows that prices have slipped by 0.3% while Nationwide suggests they have fallen by 0.9%.
Russell Quirk, director, low-cost online estate agents, eMoov.co.uk, said: "You'd be two sandwiches short of a picnic if you took this 1% rise in house prices as a sign of market strength.
"There are a couple of economic positives in the form of falling inflation and unemployment but the market is still on a knife-edge.
"Anyone looking to sell in the current market has to put their property on at the right price, or be prepared to wait indefinitely. Buyers know they have a strong hand right now. The fact that supply is even weaker than demand is supporting prices."
