Blocking Brexit was now a more likely outcome than Britain leaving the European Union without a deal, May said.
"Theresa May seems to think there is a bigger chance of no-Brexit than of no-deal Brexit. Anything that seems to reduce the chances of a 'hard' Brexit is something that would provide solace to investors," said Jane Foley, FX strategist at Rabobank.
The pound last week posted its fourth straight week in the black, rising sharply on Friday on suggestions that Britain could seek to delay its scheduled March 29 date to exit the European Union. But it has also benefited from recent dollar weakness and last week from a fall in the euro.
It rallied on Monday to a high of $1.2879, up 0.3 percent on the day while against the euro it firmed 0.2 percent to stand at 89.06 pence by 1200 GMT, the highest since Dec. 5.
However, the outlook for the currency remains uncertain -- a last-minute deal, a disorderly or no-deal exit, a new referendum or remaining in the bloc are all seen as possible. Each could have radically different consequences for the sterling outlook.
"It's difficult to know what she could say that would pull parliamentarians out of their fairly entrenched positions and into her camp," Foley added.
Instead markets are increasingly preferring to focus on signs that a "hard" Brexit -- crashing out of the bloc without a trade deal in place -- is unlikely, given parliament's growing influence on the process.
That has helped diminish expectations for sterling swings while the risk that sterling will fall against the dollar is near the lowest in more than four months, according to one-month risk reversals, a gauge of market positioning.
"We still believe there is scope for a relief pound rally in the coming months if a no-deal Brexit is avoided at the end of March," MUFG strategist Lee Hardman told clients. (Reporting by Tom Finn and Sujata Rao Editing by Jon Boyle and Raissa Kasolowsky)
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