However, the association said the reason for the increase was down to investors pulling out of money market funds, and to some extent reinvesting in equity funds.
Stripping out money market funds, the net outflow in Europe actually fell in June to just €0.2bn, down from €8bn in May.
Efama said the main reason for the easing outflows was a sharp decline in redemptions from equity funds from €11bn in May to €2bn in June
The organisation also noted that measures decided upon to strengthen the Euro area and help member countries struggling with national debt such as Greece contributed to improved investor confidence in June, leading to the reduction in outflows from long-term UCITS.
The figures also showed the value of total assets in UCITS fell by 0.4 percent in June compared to the end of May, whilst total non-UCITS rose 1.0 percent.
Efama publishes monthly fund sales data collated from 23 national fund associations.