May said she wanted an orderly departure from the European Union and planned to bring her twice-defeated divorce deal back to the British parliament. But she also warned that delaying Brexit by extending negotiations did not rule out the possibility that Britain could leave the EU without a deal.
With no consensus in Britain's parliament over how to leave the EU, May was forced to seek an extension from the EU beyond the scheduled departure date of March 29.
Markets have largely priced out the chances of a no-deal Brexit but uncertainty about how and when Britain will leave the EU have kept sterling traders on edge.
The pound dropped to as low as $1.3147, down nearly one percent on the day. It had been trading around $1.3220 before May addressed parliament, having rallied to a 9-month high of nearly $1.34 last week.
Against the euro, sterling fell 1 percent to 86.39 pence , the lowest since March 12.
The extension, which will need approval from EU member states, leaves the Brexit divorce uncertain, with options including leaving with May's deal, a longer delay, a disruptive exit or even another referendum.
"Until some clarity emerges, we do not advocate taking directional views on sterling and advise hedging downside risks, but we note that sterling has tended to react positively to events that point to a substantial delay," UBS strategists said.
Various gauges of market volatility in the pound remained firm, even as other gauges, such as one-month euro volatility indexes, ticked lower.
British government bond yields also fell, with the 30-year gilt yield hitting its lowest since September 2017 after May spoke to parliament.
Earlier, official data showed British inflation ticked up last month but stayed close to January's two-year low. As with most economic data releases, the numbers had little impact on a pound preoccupied with Brexit headlines.
Consumer prices rose at an annual rate of 1.9 percent in February after a 1.8 percent increase in January, the Office for National Statistics said. A Reuters poll of economists had forecast an unchanged rate of inflation.