By Laila Kearney

New York (Reuters) - Stock indexes around the globe weakened on Tuesday, European assets sold off and Italy's bond yields hit multi-year highs after an Italian lawmaker made anti-euro comments, though Wall Street's blue-chip index bucked the trend and set a new record.

The MSCI world equity index dipped 0.33 percent, paring Monday's gains that followed the new U.S.-Mexico-Canada trade deal. The pan-European FTSEurofirst 300 index lost 0.57 percent.

Two of Wall Street's three major indexes closed lower on Tuesday, but shares of companies including Boeing and Caterpillar CAT.N pushed up the Dow, which closed at a fresh record high. [.N]

The Dow Jones Industrial Average rose 122.73 points, or 0.46 percent, to end at 26,773.94, the S&P 500 dipped 1.16 points, or 0.04 percent, to 2,923.43 and the Nasdaq Composite dropped 37.76 points, or 0.47 percent, to close at 7,999.55.

In Italy, the economics spokesman for the country's ruling League party, Claudio Borghi, said in a radio interview that most of the country's problems could be solved by having its own currency.

His comments drove Italian 10-year bond yields to a new 4-1/2-year high, pushing the yield spread between Italian debt and German Bunds to their widest in over five years.

Shares in Italian banks, which have large sovereign bond holdings, hit a 19-month low before recovering some of their losses.

"We are dealing with a war of words, with the euro on one side and Italy on the other," said Valentin Marinov, Credit Agricole's head of G10 FX Strategy. "There's a lot of headline risk about."

Borghi and Italian Prime Minister Giuseppe Conte backed down, calling the euro "unrenounceable", helping to calm markets and erasing losses for Italy's FTSE MIB.

The euro fell to its weakest since Aug. 21 at $1.1505, before retracing to $1.1551, down 0.22 percent on the day.

The single currency has been hurt by concerns that a significant increase in the Italian budget will deepen the country's debt and deficit problems, and by extension those of the European Union.

In Asia, stocks were lower as the lift from the agreement to save the North American free trade deal faded. The deal had boosted optimism for a resolution of a trade row between the United States and China.

China's financial markets are closed for the week of Oct. 1-5 for national holidays, but data showing weaker factory growth in China hit Hong Kong stocks.

The United States and Canada forged a last-minute deal on Sunday to salvage a trilateral pact with Mexico, rescuing a $1.2 trillion open-trade zone that had been about to collapse after nearly a quarter century in operation.

The trade pact helped the dollar index rise to 95.744 - its highest since Aug. 21 - and it was last up 0.17 percent.

The dollar's strength weighed on the leading emerging markets stock index, which fell 1.2 percent, setting it on course for its biggest one-day loss for a month.

Gold rose to its highest level in more than a week as investors sought refuge in the safe haven after equity markets weakened. Spot gold added 1.3 percent to $1,202.69 an ounce. U.S. gold futures gained 1.32 percent to $1,207.40 an ounce.

Oil prices eased slightly on Tuesday, remaining close to four-year highs on worries that global supplies will drop due to Washington's sanctions on Iran.

Brent fell 18 cents to settle at $84.80 per barrel, a day after reaching a four-year high of $85.45. U.S. West Texas Intermediate (WTI) crude futures settled 7 cents lower at $75.23 a barrel, after earlier touching a four-year high of $75.91. [O/R]

"This is the market catching its breath," said Gene McGillian, director of market research at Tradition Energy in Stamford, Connecticut, as the market steadied after rallying in three consecutive sessions.

(For graphic on world forex rates in 2018, click http://tmsnrt.rs/2egbfVh)

(Additional reporting by Helen Reid in London, Karen Brettell in New York, Sethuraman N R in Bengaluru; editing by Louise Ireland, Susan Thomas, Frances Kerry and G Crosse)