* 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 (New throughout, updates prices to reflect afternoon U.S. trading)
By Trevor Hunnicutt
NEW YORK, Aug 28 (Reuters) - A global stocks index advanced to more than five-month highs on Tuesday, the day after a U.S.-Mexico trade deal boosted investor confidence.
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 risen recently on safe-haven buying by investors nervous about 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 .
"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 rose 0.16 percent, adding to Monday's biggest gain in over four months.
The Dow Jones Industrial Average rose 40.74 points, or 0.16 percent, to 26,090.38, the S&P 500 gained 2.07 points, or 0.07 percent, to 2,898.81 and the Nasdaq Composite added 13.36 points, or 0.17 percent, to 8,031.25.
Benchmark 10-year U.S. Treasury notes fell 9/32 in price to yield 2.8804 percent, from 2.85 percent late on Monday.
Trade disputes 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 the 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.
U.S. 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 said on Monday it could impose duties on that Chinese steel wheels exports, which it said were heavily subsidized.
Some emerging markets are being supported for now by the greenback's pullback from 14-month highs.
The dollar index was down 0.24 percent, just off one-month lows. Currencies such as South Africa's rand and the Australian dollar have climbed further off multi-month troughs.
The Mexican peso lost 1.05 percent versus the U.S. dollar after hitting 2-1/2 week highs following the trade deal.
The Turkish lira fell another 2.45 percent against the dollar, adding to Monday's 2 percent fall as concerns have not abated about Turkey's rift with Washington and its resistance to raising interest rates. Argentina's peso hit a record low against the dollar, marking new struggle for that developing economy.
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.
Reporting by Trevor Hunnicutt; Additional reporting by Sujata Rao in London and Swati Pandey in Melbourne; Editing by Dan Grebler and David Gregorio