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 near four-week lows. 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 0.08 percent, adding to Monday's biggest gain in over four months.

The Dow Jones Industrial Average rose 14.38 points, or 0.06 percent, to 26,064.02, the S&P 500 gained 0.78 points, or 0.03 percent, to 2,897.52 and the Nasdaq Composite added 12.14 points, or 0.15 percent, to 8,030.04.

Benchmark 10-year U.S. Treasury notes fell 9/32 in price to yield 2.8822 percent.

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 party to the North American Free Trade Agreement, and U.S.-Canada talks were set to resume 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.

THE DOLLAR AND EMERGING MARKETS

Emerging markets are looking to a pullback from the dollar from 14-month highs for some support. The dollar index was down 0.07 percent, just off one-month lows.

Yet the Mexican peso lost 1.65 percent versus the U.S. dollar after hitting 2-1/2 week highs following the trade deal.

The Turkish lira fell another 2.69 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 struggles 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.

(Graphic: MSCI All Country World Index Market Cap: http://tmsnrt.rs/2EmTD6j)

(Graphic: Global assets in 2018: http://tmsnrt.rs/2jvdmXl)

(Graphic: Global currencies vs. dollar: http://tmsnrt.rs/2egbfVh)

(Graphic: Emerging markets in 2018: http://tmsnrt.rs/2ihRugV)

(Reporting by Trevor Hunnicutt; Additional reporting by Sujata Rao in London and Swati Pandey in Melbourne; Editing by David Gregorio and Lisa Shumaker)

By Trevor Hunnicutt