"The collective decision of cabinet was that the government should agree the draft withdrawal agreement and the outline political declaration," May said after a five-hour cabinet meeting.
It is unclear whether she has enough votes to clinch approval in parliament.
"The real challenge is the parliament," said Marc Chandler, chief market strategist at Bannockburn Global Forex LLC in New York. "The hard work really lies ahead."
Hopes the U.K. parliament would approve a draft accord for Britain to leave the European Union have bolstered the pound and provided some support for the euro.
The single currency has been under pressure down by uncertainty on how EU officials would react to Italy's latest fiscal proposal after they rejected a version of it last month for violation of certain EU rules.
Italy re-submitted its draft budget for next year to the European Commission with the same growth and deficit assumptions but with falling debt, the new draft showed.
At 3:49 p.m. (2049 GMT), the euro was up 0.34 percent at $1.13255, erasing an earlier loss tied partly to weak regional growth data.
Euro zone growth rose by 0.2 percent in the third quarter, official data showed, confirming its earlier preliminary flash estimate from Oct. 30.
Against sterling, the single currency was down 0.07 percent at 86.99 pence.
The pound was up 0.39 percent at $1.302.
The euro and sterling briefly turned negative after a BBC political editor said on Twitter that May might face a no confidence vote on Thursday.
The strength in both the euro and pound pushed the dollar lower. The greenback retreated further from a 16-month peak against a basket of currencies.
Traders brushed off a government report on US consumer prices that showed domestic inflation grew at a moderate annual pace in October, although they recorded their biggest monthly increase in nine months as expected.
An index that tracks the dollar versus a basket of six major currencies was down 0.45 at 96.867 after hitting a 16-month high of 97.693 on Monday.
Among other major currencies, the Swedish crown was little weaker on the day after losing as much as 0.7 percent versus the euro to 10.2768 crowns after weaker-than-expected inflation.