Trading was volatile as concerns rose that she is likely to be succeeded by a Eurosceptic leader, potentially increasing the chances of a 'no-deal' Brexit.
"The pound can therefore breathe a sigh of relief temporarily, and it now remains to be seen how her successor will position himself," said Marc-André Fongern, a strategist at MAF Global Forex in Frankfurt.
While there is no clarity on who her successor will be, markets are concerned that a tougher stance with the European Union might prompt investors to turn more negative on the outlook for the pound in the coming months.
Those concerns have pulled the rug from under the pound over the last two weeks, prompting traders to sell the currency against the euro and the dollar aggressively and dialling up expectations of Britain crashing out of the EU without a deal.
"None of this should come as a surprise to currency markets, and as such should already be priced in, with the pound already looking a little firmer in early trading," said Michael Hewson, chief markets analyst at CMC Markets based in London.
Against the dollar, the pound was 0.4pc higher at $1.2713 after her announcement.
Versus the euro, the pound was a third of a percent stronger at 88.05 pence after 14 consecutive days of losses as traders trimmed back some of their negative bets on the pound before a long weekend.
Britain's markets are shut on Monday for a holiday.
Recent falls in the pound have been pronounced because investors have cut back their positions on the pound to neutral, removing any potential support for the British currency.
See graphic Still, derivative markets were broadly quiet with risk reversals on the pound holding near recent lows while one-month volatility indicators remained subdued.
The leading contenders to succeed May all want a tougher divorce deal, although the EU has said it will not renegotiate the Withdrawal Treaty it sealed in November.
Boris Johnson, the face of the official Brexit campaign in 2016, is the favourite to succeed May.
Betting markets put a 40pc implied probability on Johnson winning the top job.
Strategists at OANDA, a futures brokerage, say if Boris Johnson becomes the next prime minister, the pound could fall as far as $1.20, a level not seen since the first quarter of 2017.