* U.S. stocks flat as Italy worries weigh
* Euro weakens to 6-week low; Italian concerns weigh
* European stocks fall on anti-euro rhetoric
* Italian bond yields rise, bank stocks sink
* Gold jumps over 1 pct as equity sell-off triggers safe-haven bids
* Oil near 4-year highs
* Graphic: World FX rates in 2018 tmsnrt.rs/2egbfVh
By Laila Kearney
New York, Oct 2 (Reuters) - Stocks weakened around the globe and European assets sold off on Tuesday as anti-euro comments by an Italian lawmaker sent Italy's bond yields to multi-year highs and optimism over an agreement to revamp a North American trade deal receded.
The MSCI world equity index dipped 0.3 percent, paring Monday's gains due to the new U.S.-Mexico-Canada trade deal. The pan-European FTSEurofirst 300 index lost 0.55 percent.
Wall Street slipped at the open with bank stocks the biggest drag, but soon regained some momentum. The Dow Jones Industrial Average rose 81.53 points, or 0.31 percent, to 26,732.74, the S&P 500 lost 0.11 points, or -0.00 percent, to 2,924.48 and the Nasdaq Composite dropped 8.49 points, or 0.11 percent, to 8,028.82.
The economics spokesman for Italy'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 spread between Italian and German yields to the widest for more than five years.
Shares in Italian banks, which have large sovereign bond holdings, hit a 19-month low before recovering part of their losses. "We are dealing with a war of words, with the euro on one side and Italy on the other," Credit Agricole head of G10 FX Strategy Valentin Marinov said. "There's a lot of headline risk about."
Borghi and 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 $1.1537, down 0.34 percent on the day.
The single currency has been hurt by concerns that a significant increase in the Italian budget will deepen Italy's debt and deficit problems, and by extension the European Union's.
Asian stocks were lower as the boost from the agreement to save the North American free-trade deal faded. The deal lifted 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 also hit Hong Kong stocks.
The U.S. and Canada forged a last-minute deal on Sunday to salvage NAFTA as 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 its highest since Aug. 21, at 95.744. It was last at 0.17 percent.
The dollar's strength weighed on the leading emerging markets stock index, which fell 1.3 percent, setting it on course for its biggest one-day loss for a month.
Gold rose as investors sought refuge in the safe-have after equity markets weakened. Spot gold rose 1.6 percent to $1,206.11 per ounce, reaching its highest point since Sept. 21. U.S. gold futures were up 1.5 percent at $1,209.20.
Oil prices steadied near their highest since November 2014 as markets braced for tighter supply once U.S. sanctions against Iran kick in next month.
U.S. crude fell 0.31 percent to $75.07 per barrel and Brent was last at $84.77, down 0.25 percent on the day.
Additional reporting by Helen Reid in London, Karen Brettell in New York, Sethuraman N R in Bengaluru Editing by Louise Ireland and Susan Thomas