The euro zone's central bank will need to ease policy again, possibly through new rate cuts or asset purchases, if inflation doesn't head back to its target, Draghi told the ECB's annual conference in Sintra, Portugal.
That exacerbated the dash for bonds, already in play as investors fret about the world economy, the impact of trade wars and the simmering Iran-US tensions in the Gulf.
Germany's 10-year government bond yield, the benchmark for the bloc, dropped five basis points to a new record low of minus 0.30% after the remarks, while most other euro zone bond yields slipped 5-10 basis points on the day.
Austrian 10-year yields slipped into negative territory for the first time ever, while the Draghi effect also sent US 10-year Treasury yields to their lowest since September 2017.
"He has been quite bold -- not that all these measures were not already hinted at, but today is probably the first time we hear directly from Draghi that all these tools are considered available," said UniCredit rates strategist Luca Cazzulani.
"We are facing a difficult situation globally and inflation expectations in the euro zone are extremely low. Also, the markets are pricing in bold action from the Fed; in this environment it is difficult for the ECB to stand still."
As if to underline this, a closely watched survey by the ZEW Institute showed the mood among German investors deteriorated sharply in June.
Money market investors are now fully pricing in an ECB rate cut for December 2019 for the first time.
Just two weeks ago, they were pricing in a 60% chance of a rate cut by the end of the year.
The euro weakened across the board, falling to a two-week low versus the dollar and to a 1-1/2 week low versus the Swiss franc.
The main euro zone stocks index trimmed early losses as the euro fell. It was trading down just 0.1% by 0812 GMT as the fall in the single currency translated into a boost for euro zone exporters.
Inflation expectations, on the other hand, were boosted by talk of more stimulus, with key market gauge the five-year, five-year breakeven rate rising sharply to 1.2017% from 1.144% on Monday.
Italian debt outperformed, with yields dropping 7-12 bps across the curve; the euro zone's third-largest economy is seen as one of the biggest beneficiaries of ECB largesse.
These yields may have also been pushed lower by some conciliatory comments from Finance Minister Giovanni Tria.
Tria said Italy will cut spending to meet its fiscal deficit targets this year and can reach an agreement with the European Commission over its budget plans.