In an interview with the Financial Times, Draghi said that the need for fiscal policy as a complement to monetary policy was now more urgent than before.
The ECB unleashed a fresh round of stimulus on Sept. 12, but concern is growing that the bank is reaching the limits of what it can achieve without governments doing more through fiscal policy.
This has contributed to selling this month in higher-rated debt markets such as Germany, France and the Netherlands.
"It's very clear that the ECB has no power over the fiscal side," said Peter Chatwell, head of rates at Mizuho.
Most 10-year bond yields rose 2-3 basis points, though weak inflation prints from Spain and German states limited the sell-off in bond markets.
Germany's 10-year bond yield rose to a one-week high at -0.54%, while 30-year bond yields were 5 bps higher on the day at -0.07%.
Long-dated bond yields in Germany and France have risen by about 15 bps this month, set for their biggest monthly rise since early 2018.
A key market gauge of long-term inflation expectations in the single currency bloc fell to 1.169%, its lowest since early July, after the Spanish and German data.
As the third quarter drew to a close, Italy stood out as the bloc's best-performing bond market.
Italy's 10-year bond yield, which moves in the opposite direction to the price, is down 18 bps this month at 0.85% and a hefty 125 bps this quarter -- set for its biggest quarterly slide since early 2012.
The formation of a new coalition government comprising the 5-Star Movement and pro-European Democratic Party in August has dispelled near-term election risks, driving investors into one of the few positively yielding bond markets in the single currency bloc.
Italy is also seen as a key beneficiary of the latest ECB stimulus, which includes open-ended asset purchases, while concerns about the country leaving the bloc have fallen away.
Italy's economy minister suggested on Sunday that the country's budget deficit would be set at about 2.2% of domestic output next year, emphasising the need for flexibility as Rome tries to rekindle stalled growth without reigniting friction with the EU.
"The Italian coalition has been taken relatively well, but it very important to watch the internal discussions on the budget," said Ross Hutchison, a fixed-income fund manager at Aberdeen Standard Investments.
Austria's bond market showed little immediate reaction to news that conservative leader Sebastian Kurz triumphed in Sunday's parliamentary election.