Sterling bobbed briefly above $1.31 in late morning foreign exchange deals, while the euro dipped versus the pound.
Asian and European stock markets mostly pushed higher, on the eve of a vital European Union summit where the bloc's leaders will discuss May's request to push Brexit back to June 30.
In a whirlwind tour on Tuesday, the British premier will meet Chancellor Angela Merkel in Berlin and President Emmanuel Macron in Paris in a last-gasp bid to keep her country from crashing out on Friday.
"The pound appears to be pre-disposed to seeing good news," Rabobank analyst Jane Foley told AFP.
"The fact that May has more key talks scheduled is been taken as a indication that a delay could be agreed to push the Brexit start date beyond April 12."
May asked EU leaders on Friday to delay Brexit until late June to give her time to strike a compromise with the opposition that lets Britain's hung parliament back an orderly divorce plan on the fourth attempt.
The 27 European leaders have already signed off on one extension -- the original deadline was March 29 -- while many investors expect that a no-deal Brexit will still be averted.
"There has been an optimistic bias in the pound that dates back to before the 2016 (Brexit) referendum," Foley added.
"The market consensus has suggested for months that a no deal Brexit will be avoided and this bias is reflected in the fact that the pound is the best performing G10 currency in the year to date."
Adding to concern is the fact May is also facing a revolt by pro-Brexiters within her Conservative Party over her decision to hold talks with the opposition Labour Party.
Markets meanwhile remain on tenterhooks on the eve of the European Central Bank's latest interest rate decision -- and publication of the US Federal Reserve's latest meeting minutes.
"Investors are waiting for the next catalyst before considering extending current gains," added London Capital Group analyst Jasper Lawler.
While the broad equities trend remains upwards, sentiment was given a knock by news that US President Donald Trump had trained his sights on the EU by threatening tariffs on billions of dollars' worth of goods.
Earnings season also kicks off in earnest this week, with expectations low but observers hoping for some positive forward guidance.
- Key figures around 1030 GMT -
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Pound/dollar: UP at $1.3080 from $1.3061 at 2100 GMT on Monday
Euro/pound: DOWN at 86.19 pence from 86.23 pence
Euro/dollar: UP at $1.1276 from $1.1263
Dollar/yen: DOWN at 111.29 yen from 111.48 yen
London - FTSE 100: UP 0.1 percent at 7,458.26 points
Frankfurt - DAX 30: FLAT at 11,966.51
Paris - CAC 40: UP 0.1 percent at 5,478.52
EURO STOXX 50: UP 0.2 percent at 3,444.07
Tokyo - Nikkei 225: UP 0.2 percent at 21,802.59 (close)
Hong Kong - Hang Seng: UP 0.3 percent at 30,157.49 (close)
Shanghai - Composite: DOWN 0.2 percent at 3,239.66 (close)
New York - Dow: DOWN 0.3 percent at 26,341.02 (close)
Oil - Brent Crude: UP 16 cents at $71.27 per barrel
Oil - West Texas Intermediate: UP 27 cents at $64.67