* Shares in Europe fall into red
* Investors flock to safe haven assets
* Pound reverses course after UK's Cox comments
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By Josephine Mason
LONDON, March 12 (Reuters) - A rally across global stocks and sterling triggered by last-minute tweaks to Britain's deal to exit the European Union evaporated on Tuesday as comments from the government's top lawyer raised fresh doubts the new terms won't sway lawmakers.
Sterling and European stocks rallied after Brussels agreed to last-minute changes to an updated Brexit deal with British Prime Minister Theresa May on Monday night, raising hopes the government would secure a deal before the Brexit deadline in less than three weeks.
But markets rapidly reversed course midmorning after Britain's Attorney General Geoffrey Cox said the legal risks to the Irish backstop, or protocol, remained unchanged despite assurances from the European Union.
His comments reignited worries that the latest tweaks would not be enough to woo rebellious British lawmakers who have threatened to vote down May's plan again on Tuesday evening, raising the chances of a no-deal exit that have unnerved financial markets in recent months.
The pan-European STOXX 600 was down 0.2 percent, having rising as much as 0.4 percent earlier, while sterling fell as much as 1.2 percent against the euro, which would have put it on track for its biggest fall since November.
The currency was down 0.8 percent and 0.7 percent against the U.S. dollar and the yen respectively.
Securing a deal to avoid crashing out of the EU or delaying the process would eliminate one of the three major concerns of global investors, alongside trade and slowing global growth.
But Chris Scicluna, head of economic research at Daiwa Capital Markets, said it was difficult to see how pro-Brexit members of parliament would back the deal following Cox's comments.
"If May goes ahead with the vote tonight given the Cox opinion, she will face a sizeable defeat, perhaps over 100 votes," he said.
Waning enthusiasm also tempered Wall Street gains, with futures also fading ahead of inflation data.
Britain's blue chip FTSE 100 benefited from the sudden about-turn in the local currency, reversing earlier losses and gaining 0.2 percent. With 70 percent of its income coming from abroad, the blue chip index is often pressured by a stronger pound.
"This additional agreement to the existing contract does slightly increase the probability that by tonight the deal will go through, but only slightly increases it," said Britt Weidenbach, head of European equities at DWS.
"The market will probably only react to this in a more positive way once we know what the outcome is going to be. This might not be after tonight, it may be after Wednesday when we have a ruling on no-deal and prolongation."
News of the assurances had buoyed Asian equities overnight. MSCI's broadest index of Asia-Pacific shares outside Japan closed up 1 percent, while Chinese blue chips ended up 0.7 percent, extending the previous day's rally.
Despite slowing domestic economic growth and uncertainty about the outlook for trade negotiations between China and the United States, Chinese markets have been buoyed this year by investors' expectations of more stimulus to cushion any downturn.
The CSI300 index has risen more than 28 percent this year.
Japan's Nikkei stock index closed 1.8 percent higher, but Australian shares erased earlier gains to end down 0.1 percent.
Cox's comments prompted investors to flock back to safe-haven German government bonds.
Germany's benchmark 10-year government bond yield was trading steady at 0.07 percent, down from 0.107 percent earlier in the day and not far off more than two-year lows hit last week at 0.048 percent.
Britain's 10-year gilt yield was also flat at 1.17 percent, having risen as much as 7 bps.
The dollar index, which measures the greenback against a basket of currencies, flat, while the safe-haven yen was up 0.1 percent against the dollar.
In commodity markets, oil prices rose on a combination of strong demand and supply cuts by the Organization of the Petroleum Exporting Countries (OPEC).
A political and economic crisis in OPEC-member Venezuela is also expected to lift crude prices.
U.S. crude was up 0.3 percent at $57.11 a barrel and Brent crude was 0.4 percent higher at $66.97 per barrel.
Spot gold was up 0.2 percent to $1,296.1 per ounce.
Reporting by Josephine Mason; Additional reporting by Helen Reid and Dhara Ranasinghe ; Editing by Alison Williams