* U.S.-Mexico deal punctures global trade war fears
* World stocks index at more than 5-month high
* U.S.-Canada talks and China leg of U.S. trade war still loom (Updates to U.S. stock market open; changes dateline; previous LONDON)
By Trevor Hunnicutt
NEW YORK, Aug 28 (Reuters) - A global stocks index advanced to more than five-month highs on Tuesday, lifted by investor optimism that a U.S.-Mexico deal will help avert a global trade war.
Monday's news of the U.S.-Mexico agreement on trade pushed the S&P 500 and Nasdaq indexes to record highs, and indexes across Europe and Asia followed Wall Street's lead, inching to multi-month highs.
The dollar, which had been a haven as investors anticipated contentious trade disputes and U.S. Federal Reserve interest rate hikes, slipped to a four-week low. Emerging market stocks hit their highest since Aug. 10 .MSCIEF .
"Global trade tensions have undoubtedly been the most significant source of risk in 2018," said Hussein Sayed, chief market strategist at FXTM.
"The U.S.–Mexico deal seemed to boost confidence that the trade war is moving closer to an end, and the next question is 'Who's next to close a deal with Trump?'" he said.
MSCI's benchmark world share index .MIWD00000PUS followed Monday's best performance in over four months with a 0.21 percent gain.
The Dow Jones Industrial Average .DJI rose 44.39 points, or 0.17 percent, to 26,094.03, the S&P 500 .SPX gained 2.16 points, or 0.07 percent, to 2,898.9 and the Nasdaq Composite .IXIC added 12.50 points, or 0.16 percent, to 8,030.39.
Benchmark 10-year notes US10YT=RR last fell 10/32 in price to yield 2.8858 percent, from 2.85 percent late on Monday.
Disputes on trade have weighed on investor sentiment for much of 2018, despite solid economic fundamentals and robust corporate earnings. Many remain cautious.
Paul Donovan, chief economist at UBS Global Wealth Management, said markets' assumption that Canada will go along with the U.S.-Mexico deal is not "zero risk." The three countries are currently part of the North American Free Trade Agreement, and U.S.-Canada talks are due later on Tuesday. President Donald Trump threatened he still could put tariffs on Canadian-made cars and demanded concessions on Canada's dairy protections.
"If Canada does not join, then getting the agreement of (U.S.) Congress (to the deal) will be trickier," Donovan said.
The toughest battle in the trade war, with China, still looms. The United States and China held two days of talks last week without a major breakthrough, as another round of tariffs took effect.
The U.S. Commerce Department also said on Monday that Chinese steel wheels exports were heavily subsidized and that it could impose duties on the product.
Asian and other emerging markets are being supported for now by the greenback's pullback from 14-month highs. The dollar index .DXY was down 0.2 percent, just off one-month lows.
U.S. economic data could determine the dollar's further moves. The latest estimates for second-quarter U.S. gross domestic product are expected on Wednesday.
The dollar's retreat has allowed currencies such as South Africa's rand ZAR=D3 and the Australian dollar AUD=D3 to rise further from multi-month troughs.
The Mexican peso, however, lost 0.72 percent versus the U.S. dollar MXN=D3 after hitting 2-1/2 week highs following the trade deal.
The Turkish lira fell another 1.8 percent against the dollar TRY=D3 , adding to Monday's 1.9 percent fall as concerns have not abated about Turkey's rift with Washington and its resistance to raising interest rates.
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