Carney said that the BoE would probably need to pump more stimulus into Britain's economy over the summer after the shock of last week's decision by voters to leave the European Union.
Investors were already expecting the BoE to cut interest rates in July or August from an already record low of 0.5 percent, and ramp up its 375 billion pound bond buying plan, too.
Sterling fell more than 1.6 percent to a session low of $1.3207
"Carney’s comments today sort of confirm the general bearish view on sterling," said Mazen Issa, senior currency strategist at TD Securities in New York. He said TD expected the BoE to cut rates by 50 basis points in August, and that the sterling would likely fall to $1.20 by the end of the year.
The euro sank against the dollar after Bloomberg reported that the ECB was considering loosening the rules for its bond purchases to ensure enough debt is available to buy following the Brexit vote, citing unnamed euro-area officials.
The euro
"You have the two major central banks in Europe once again on the quantitative easing path with renewed vigour," said Joseph Trevisani, chief market strategist at WorldWideMarkets in Woodcliff Lake, New Jersey, in reference to the BoE and ECB.
On the last day of the second quarter, the period was on track to be sterling's weakest against the dollar since the fourth quarter of 2008.
While the greenback was set to post an 8.3-percent quarterly loss against the yen, its biggest since the fourth quarter of 2008, the dollar index <.DXY> was set to gain about 1.5 percent for the quarter. The index measures the greenback against six major rivals.
(Additional reporting by Patrick Graham in London; Editing by Lisa Von Ahn and Nick Zieminski)
By Sam Forgione
