The pound retreated almost 0.1 percent to $1.2208 after both houses backed the so-called Brexit bill, opening the door for May to start the clock on the required two-year negotiation period by the end of this month.
The euro hovered at $1.0656, failing to recover any of Monday's 0.2 percent loss.
On Monday, sterling had jumped 0.36 percent after Scotland's First Minister Nicola Sturgeon demanded a new independent referendum in late 2018 or early 2019, once the terms of the UK's exit from the EU are clearer.
The MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.1 percent, while Japan's Nikkei inched down 0.1 percent.
Chinese shares saw early gains rolled back after combined retail sales for January and February rose only 9.5 percent from a year earlier, missing expectations of 10.5 percent. Fixed-asset investment expanded 8.9 percent, and industrial output grew 6.3 percent, both beating forecasts.
The CSI 300 index opened the day lower, then rose but gave back that gain after the data release.
While saying the data continues the stable trend seen in the second half of 2016, China's statistics bureau warned that the economy continues to face uncertainties, and emphasized the need to increase internal development drivers.
China has cut this year's economic growth target to about 6.5 percent to give policymakers more room to push through painful reforms to contain financial risks. The economy grew 6.7 percent in 2016, the slowest pace in 26 years.
On Monday, Goldman Sachs upgraded Chinese stocks to "overweight" on better growth prospects and a bullish view on the country's banking sector. Its strategists cited rising producer prices and easing credit stress, and a brighter credit outlook and loan pricing for banks.
Overnight, Wall Street was mixed, with the Dow Jones Industrial Average down 0.1 percent, while Nasdaq rose 0.24 percent and the S&P was little changed.
With an interest rate hike this week by the Federal Reserve fully priced in, markets are focused on signals from the U.S. central bank about the pace of future rises.
"On one hand, the market ponders a surprise hold, in which massive unwinding of positions could take place with the hike already priced in," Jingyi Pan, market strategist at IG in Singapore, wrote in an note.
"On the other hand, concerns have also been paid to an acceleration in the Fed’s path to normalisation, where the likelihood of four Fed hikes has been raised, up from the current projection of three," she said. "The immediate reaction is likely to be seen in the dollar and upsides towards December’s high on the dollar index may be eyed."
The dollar index was almost 0.1 percent higher 101.38, extending Monday's gains following a bout of profit taking at the end of last week.
The dollar was steady at 114.81 yen, but remains below the seven-week high touched on Friday on expectations of a Fed move at the end of a two-day meeting on Wednesday.
Markets are also awaiting a meeting of the Group of 20 finance ministers and central bankers in the German town of Baden Baden starting on Friday, their first meeting since Donald Trump won the U.S. presidential election.
U.S. Treasury Secretary Steven Mnuchin will be "pushing hard" to advance U.S. interests in his debut G20 meeting, including reaffirming commitments to avoid competitive currency devaluations, a senior Treasury official said on Monday.
In commodities, oil prices dipped 0.1 percent. They touched a 3-1/2-month low in the previous session as concerns about rising U.S. production offset optimism about supply cuts by the Organization of Petroleum Exporting Countries.
U.S. crude fell to $48.35, while global benchmark Brent was trading at $51.29.
Gold was in a holding pattern at $1,203.76 ahead of the Fed decision.
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