Yields initially dropped after the central bank, which kept interest rates unchanged for now, said in its statement it saw rates at present or lower levels through mid-2020, giving up a previous pledge to keep rates unchanged through next June.
It also tasked its staff to look at various other easing options including restarting asset purchases.
Draghi's comments regarding a low risk of a recession, however, changed the direction of the market.
"Although he said things such as the outlook is getting worse and worse, they still see the sign of a recession risk as pretty low, so the market is interpreting this as somewhat hawkish," said Jon Hill, an interest rate strategist at BMO Capital Markets in New York.
Benchmark 10-year Treasuries fell 14/32 in price to yield 2.097pc, after earlier falling to 2.011pc, the lowest since July 8.
Weak global growth is leading central banks to ease policy globally, with the Federal Reserve viewed as certain to cut rates when it meets next week.
Interest rate futures traders are pricing in a 79 percent chance of a 25-basis-point cut and 21 percent likelihood of a deeper 50-basis-point decrease, according to the CME Group's FedWatch tool.
The next major economic focus for the United States will be Friday's Gross Domestic Product (GDP) figures for the second quarter.
The Treasury Department will sell $32 billion in seven-year notes on Thursday, the final sale of $113 billion in short and intermediate-dated notes this week.
A $41 billion auction of five-year notes on Wednesday and a $40 billion sale of two-year notes on Tuesday both saw weak demand.