GENEVA (Reuters) - A failure of euro zone government to enact badly needed fiscal and structural reform could force the European Central Bank to ease policy further to meet its inflation mandate, Executive Board member Benoit Coeure said on Tuesday.

Growth is picking up and will continue to accelerate but the recovery is not as strong as the ECB would like and governments' fiscal policy has not matched the Bank's monetary stimulus efforts, Coeure, a top lieutenant of ECB President Mario Draghi told a conference.

Hoping to stave off deflation and kick start private sector growth, the ECB has cut rates deep into negative territory, given banks free loans and is buying 80 billion euros worth of assets per month.

But inflation in just above zero and unemployment remains high, raising the risk that the ECB will have to do even more, unless governments enact measures that boost long term growth.

"If nothing takes place (in terms of reforms,) then the central bank may have to do more," Coeure told a European Economic Assocation conference in Geneva.

"The only message here is if there is not much taking place on the structural reform front, if there is not much taking place on the fiscal policy front, from what can be done, then the ECB would have to do more."

But further ECB action would come with side effects, Coeure warned.

Sub-zero interest rates are hitting banks, which transmit the ECB's monetary policy, and ECB buying is fuelling concerns about price bubbles.

"So anything we do also comes with side-consequences - possible future risk for financial stability," Coeure said. "So far we mitigated, managed, curbed those risks."

Relatively healthy growth figures since Britain's referendum are nonetheless taking pressure off the Bank to act immediately, giving it time, possibly until its December meeting, to consider fresh measures.

Its 80 billion euro per month asset buying scheme is set to run out next March and investors argue that the bank needs to decide by December whether to continue the programme or start winding it down.

(Reporting by Stephanie Nebehay; Writing by Balazs Koranyi; Editing by Francesco Canepa/Jeremy Gaunt)