May is seeking a delay beyond April 12 to give her time to sit down with the opposition Labour Party in a bid to break the impasse over Britain's departure.
The pound rallied as much as 0.4% after May's statement, to trade above the $1.31 line. Previously, it was heading towards the $1.30 levels.
The euro jumped to a U.S. session high of $1.1215 before giving up much of the gains and remaining lower on the day.
The euro has dropped to more than three week lows against the U.S. dollar as investors evaluate international growth prospects with the U.S. and European central banks unlikely to raise interest rates soon.
Survey data on Monday showed factories in the euro zone had their worst month in almost six years in March, while economic data in the United States offered more hope.
Data on Tuesday, however, showed that new orders for key U.S.-made capital goods unexpectedly fell in February and shipments were unchanged, while data for January was revised slightly higher.
"The theme is really is good U.S. data good or bad for the dollar?” said Mark McCormick, North American head of FX strategy at TD Securities in Toronto, adding that it may in fact be negative with the Federal Reserve on hold regarding rates.
That is because a solid U.S. economy should help the view that the global economy will stabilize, and encourage investors searching out yield to move into emerging markets for higher returns, he said.
Outflows from European equity exchange-traded funds have also diminished, which suggests an improving outlook for the region, McCormick said. Like the Fed, the ECB is not expected to raise rates in the near term.
The single currency was last $1.1194 against the dollar, after earlier dipping to $1.1181, the lowest since March 7. The euro is nearing the $1.1174 level, which if broken would send the currency to its weakest levels since June 2017.
Some technical indicators suggest the euro may be nearing the end of its downturn, and that it should find support soon if it does not drop below the $1.1185-$1.1175 region.
The euro is trying to find a bottom, "but (it) needs to do more work," Karen Jones, a technical analyst at Commerzbank wrote on Tuesday in a report.
Australia's dollar shed 0.69% after the Australian government downgraded its growth forecasts but said it expected the economy to extend its enviable recession-free run of growth into a third decade.
Currency bid prices at 2:06PM (1806 GMT)
Description RIC Last U.S. Close Pct Change YTD Pct High Bid Low Bid
Euro/Dollar EUR= $1.1194 $1.1212 -0.16% -2.40% +1.1218 +1.1184
Dollar/Yen JPY= 111.3400 111.3400 +0.00% +0.98% +111.4500 +111.2600
Euro/Yen EURJPY= 124.68 124.84 -0.13% -1.22% +124.9000 +124.4800
Dollar/Swiss CHF= 0.9984 0.9987 -0.03% +1.73% +1.0000 +0.9974
Sterling/Dollar GBP= 1.3114 1.3099 +0.11% +2.80% +1.3131 +1.3015
Dollar/Canadian CAD= 1.3351 1.3306 +0.34% -2.10% +1.3374 +1.3305
Australian/Doll AUD= 0.7062 0.7111 -0.69% +0.20% +0.7129 +0.7053
Euro/Swiss EURCHF= 1.1180 1.1197 -0.15% -0.66% +1.1203 +1.1169
Euro/Sterling EURGBP= 0.8534 0.8558 -0.28% -5.01% +0.8607 +0.8531
NZ NZD= 0.6744 0.6804 -0.88% +0.40% +0.6804 +0.6740
Dollar/Norway NOK= 8.6107 8.5810 +0.35% -0.32% +8.6301 +8.5872
Euro/Norway EURNOK= 9.6410 9.6253 +0.16% -2.68% +9.6581 +9.6212
Dollar/Sweden SEK= 9.3310 9.2810 +0.39% +4.10% +9.3427 +9.2840
Euro/Sweden EURSEK= 10.4479 10.4068 +0.39% +1.79% +10.4535 +10.4039
All spots FX=
Tokyo spots AFX=
Europe spots EFX=
Tokyo Forex market info from BOJ TKYFX World central bank news CEN
Economic Forecasts... ECON Official rates...INT/RATE
Forex Diary.......MI/DIARY Top events........M/DIARY
Diaries...........DIARY Diaries Index........IND/DIARY
Press Digests.....PRESS Polls on G7 economies..SURVEY/
(Additional reporting by Tommy Wilkes in London; editing by James Dalgleish and Diane Craft)
By Karen Brettell