The problem is there’s nothing he can do about it short of backing off on supporting fiscal austerity.

Buying fx is not an option ideologically, as it would give the appearance that the fx reserves are backing the euro.

Late addition:
One more thing, Japanese buying of member nation euro bonds necessarily weakens the yen.

So does Draghi want that to stop/rates to go up?

Draghi Signals Euro Strength May Hurt ECB’s Recovery Efforts

By Matthew Brockett and Stefan Riecher

Feb 7 (Bloomberg) — “The exchange rate is not a policy target, but it is important for growth and price stability,” ECB President Mario Draghi said at a press conference. “We want to see if the appreciation is sustained, and if it alters our assessment of the risks to price stability.” Draghi noted that the ECB will publish new economic projections next month and stressed that officials will “maintain our accommodative monetary stance.” Draghi said economic weakness will prevail only “in the early part” of this year and “later in 2013, economic activity should gradually recover, supported by our accommodative policy stance.” Still, risks to the economic outlook remain on the downside, he said. Draghi said if monetary policies produced “consequences on the exchange rate that do not reflect the G-20 consensus, we will have to discuss this.”