The prospect of another delay had initially hit sterling, which briefly dropped as low as $1.2841 on Wednesday in Asian trade before bouncing back to over $1.2890, up from late in New York on Tuesday.
The pound is experiencing volatility on every Brexit twist and turn. Earlier this week the unit reached five-month highs above $1.30 on increasing hopes that a painful 'no-deal' Brexit divorce would be averted.
"Like Brexit, the pound is bouncing around," said CMC Markets UK analyst David Madden.
"Traders are terrified at the prospect of a no-deal Brexit, but that currently seems very unlikely, which is assisting the pound," he added.
In stock market trading, London's benchmark FTSE 100 index climbed 0.7 percent, while eurozone equities were mixed.
The EU is set to grant another Brexit extension after British MPs on Tuesday rejected Prime Minister Boris Johnson's bid to force his divorce deal through parliament this week.
European Council President Donald Tusk has recommended that the EU's 27 other member states grant an extension, likely until the end of January.
In the meantime, the UK could hold a general election aimed at ending the Brexit deadlock, according to analysts.
Elsewhere on Wednesday, Wall Street moved higher, with the Dow up 0.3 percent in midday trading.
Shanghai's main stocks index closed down 0.4 percent and Hong Kong lost 0.8 percent, with traders keeping tabs on reactions to a Financial Times report saying China is drawing up a plan to remove Hong Kong's beleaguered chief executive after nearly five months of pro-democracy unrest.
In commodities trading, oil prices bounced higher after data indicated US oil and gasoline stockpiles decreased, easing worries about weak crude demand growth as the world economy slows.
On the corporate front, shares in French carmaker PSA jumped 3.2 percent after the company said healthy demand for upmarket models helped it resist a slowdown in the global automotive market.
The maker of Peugeot, Citroen, DS, Opel and Vauxhall vehicles announced a one-percent gain in third-quarter sales to 15.6 billion euros ($17.4 billion).
Meanwhile shares in Boeing climbed 3.0 percent despite reporting that third-quarter profits fell by half to $1.2 billion as it said it expects to get regulatory approval this year to return the grounded 737 MAX to service.
"Dow component Boeing's profit miss is being shrugged off as the company stuck to its plan to return the 737 MAX to service" by the end of the fourth quarter, said analysts at Charles Schwab brokerage.
Key figures around 1530 GMT
Pound/dollar: UP at $1.2886 from $1.2872 at 2100 GMT
Euro/pound: DOWN at 86.31 pence from 86.43 pence
Euro/dollar: DOWN at $1.1121 from $1.1125
Dollar/yen: UP at 108.63 yen from 108.49 yen
London - FTSE 100: UP 0.7 percent at 7,260.74 points (close)
Paris - CAC 40: DOWN less than 0.1 percent at 5,653.44 (close)
Frankfurt - DAX 30: UP 0.3 percent at 12,798.19 (close)
EURO STOXX 50: UP less than 0.1 percent at 3,607.65
New York - Dow: UP 0.3 percent at 26,870.20
Tokyo - Nikkei 225: UP 0.3 percent at 22,625.38 (close)
Hong Kong - Hang Seng: DOWN 0.8 percent at 26,566.73 (close)
Shanghai - Composite: DOWN 0.4 percent at 2,941.62 (close)
Brent North Sea crude: UP 1.0 percent at $60.30 per barrel
West Texas Intermediate: UP 1.3 percent at $55.19 per barrel