* Pound up more than 2 pct from Monday's lows
* Yen weakens as broader market sentiment improves
* Swedish crown in focus for inflation data
* Graphic: World FX rates in 2019 tmsnrt.rs/2egbfVh (Writes through, adds details, analyst quote)
By Tommy Wilkes
LONDON, March 12 (Reuters) - The dollar fell on Tuesday after an apparent breakthrough in Brexit negotiations between the European Union and Britain encouraged buying of riskier currencies.
The yen was also lower as investors' mood turned positive following news that British Prime Minister Theresa May had secured legally binding assurances from the EU hours ahead of a parliamentary vote on her Brexit withdrawal deal.
With the future of the Brexit deal still hanging in the balance, lawmakers were studying the assurances with lawyers prior to the move.
Sterling at one point had added more than three cents versus the dollar from its Monday's lows while against the euro it hit a 22-month high.
"The positive risk mood is into a second day as optimism about U.S./Chinese trade, a lack of fresh news and Brexit optimism (for once) conspire to keep yen, Swissie, and dollar anchored," said Kit Juckes, a strategist at Societe Generale.
The dollar index fell 0.3 percent against a basket of currencies, to 96.838.
The Japanese yen, usually popular when investors turn nervous, also dropped, losing 0.2 percent to 111.425 yen .
The euro rose 0.3 percent to $1.1282, recovering more ground after falling last week when the European Central Bank announced a delay to raising interest rates.
The improved mood, also helped by renewed hopes for a U.S.-China trade deal and firm U.S. retail sales data on Monday, supported emerging market currencies.
Sweden's crown fell after February inflation came in slightly below expectations. The crown later recovered, settling at 10.57 crowns per euro, down 0.2 percent on the session.
The Norwegian crown strengthened further after a positive central bank activity survey. It had firmed 0.8 percent against the single currency on Monday after strong inflation data fanned expectations of an interest rate rise.
But it was sterling that was the standout mover.
It rose 0.6 percent to $1.3232, having hit a high of $1.3290 overnight after falling as low as $1.2945 on Monday.
Against the euro too, sterling performed well, adding 0.4 percent to 85.15 pence per euro after earlier touching 84.755 pence.
Britain's parliament voted down May's initial deal by a record 230 votes in January, and sterling is likely to be sensitive to any signs the prime minister can convince enough lawmakers to switch sides on Tuesday.
Britain's scheduled departure from the EU is March 29 and while fears of a no-deal Brexit have receded, investors still do not know how and when Britain will exit the trading bloc.
"Having lost the first vote by a margin of 230, approval of the Withdrawal Deal would be a huge surprise tonight and could send GBP/USD to $1.35. Elevated levels of short-term volatility suggest that is possible, though perhaps not likely," ING analysts wrote to clients.