The report found that new seller asking prices are at a virtual standstill, up just 0.1% in May.
Miles Shipside, Rightmove director and housing market analyst said: “It appears that the timing of the MMR, more property for sale in all regions and a release of pent-up buyer demand are alleviating some of the upward price pressure.”
More regions experienced falls than rises, with London experiencing a decline of 0.5%.
The report suggests that the nationwide slowdown stems from a combination of buyer reluctance and a surge of over 20% more sellers rushing to market in May.
Since 2013, there has been a 9.6% year-on-year increase in new sellers, while many buyers have already bought property in 2014 causing demand to relax and buyer activity to slowdown.
The Index also suggests that in some areas, including London, prices have hit an affordability cap.
MMR is also highlighted as a factor behind slowing demand, due to a noticeable drop in mortgage approvals since its implementation.
Shipside said: “While the legacy of rises in London continues to fuel price increases in all southern regions, London itself is now marking time.
“It’s an example to the rest of the country of what happens when affordability and common sense get stretched too far.
“This will come as a relief to the governor of the Bank of England and the FPC, who have cited an overheated housing market as a serious threat to economic recovery.”
Jeremy Duncombe, director at Legal & General Mortgage Club said: “Although these figures indicate that house price growth has slowed down in June, compared to this time last year house prices have grown significantly.
“The average house price in London and the South East remains much higher than in other parts of the country, showing a regional divide is still present in the market.
“Lack of housing supply is a big issue that is hindering the market’s ability to grow in a sustainable and healthy way,” he said.
“Demand is unlikely to diminish substantially and the government needs to be meeting its housing targets and work closely with the mortgage and construction industries in order to feed this appetite.”