Sterling briefly sank below $1.27 after May announced that she would step down on June 7 as prime minister, paving the way for a brutal contest to replace her.
However, the pound did not reach the four-month lows that were plumbed a day earlier and was still higher compared to late Thursday, as dealers argued the news had already been priced in.
"The pound will bounce around here and there but it won't be going anywhere fast," Forex.com analyst Fawad Razaqzada told AFP.
"A lot now depends who will be the next leader of the Tories."
The currency could face fresh turmoil with key Brexiteer and former foreign minister Boris Johnson the front-runner to replace May.
Ratings agency Moody's warned that news of May's departure "amplifies the uncertainty" over Britain's withdrawal from the European Union -- and "increases the risk of a no-deal Brexit".
- Olive branch -
================
Elsewhere, Europe's major stock markets rebounded on Friday after the previous day's sharp-selloff that was sparked by the China-US trade war and global economic worries.
Sentiment brightened after Trump declared that there is a "good possibility" Washington will reach an agreement with Beijing to end their trade conflict, adding that "it's possible that Huawei would be included in a trade deal".
Fiona Cincotta, analyst at trading firm City Index, said that equities had won support on "Trump's trade olive branch" to China.
"President Trump's softening stance on Huawei and more positive comments on the US-China trade negotiations helped" markets move higher, she added.
However, investors remain anxious over ongoing European Parliament elections that could see big gains for populist forces.
Global equities had slumped Thursday in what one analyst called a "perfect storm" of Europe elections, fresh economic gloom, May's decision to delay a key Brexit vote and the China-US trade war.
Trump's remarks have however sparked hope of a breakthrough at the next G20 gathering in Japan next month.
Tensions between China and the US have ramped up ever since Trump banned Chinese telecoms giant Huawei from the US market and prevented American firms from selling to it.
Oil rose Friday, but only made a dent in the huge falls suffered the day before over concerns about the impact of the trade war on energy demand.
Uncertainty on trading floors has also fuelled a rally in bonds this week, with yields on the 10-year Treasury touching their lowest level in 19 months, indicating rising demand for the safe-haven assets.
- Key figures around 1100 GMT -
===============================
Pound/dollar: UP at $1.2704 from $1.2657 at 2100 GMT
Euro/pound: DOWN at 88.08 pence from 88.34 pence
Euro/dollar: UP at $1.1188 from $1.1181
Dollar/yen: DOWN at 109.68 yen from 109.61 yen
London - FTSE 100: UP 0.7 percent at 7,278.02 points
Frankfurt - DAX 30: UP 0.9 percent at 12,057.44
Paris - CAC 40: UP 0.9 percent at 5,329.24
EURO STOXX 50: UP 1.0 percent at 3,361.28
Tokyo - Nikkei 225: DOWN 0.2 percent at 21,117.22 (close)
Hong Kong - Hang Seng: UP 0.3 percent at 27,353.93 (close)
Shanghai - Composite: FLAT at 2,852.99 (close)
New York - Dow: DOWN 1.1 percent at 25,490.47 (close)
Oil - Brent Crude: UP 74 cents at $68.50 per barrel
Oil - West Texas Intermediate: UP 67 cents at $58.58