* European stocks follow Asia lower
* Italian bond yields rise, bank stocks sink
* Oil near 4-year highs
* Graphic: World FX rates in 2018 tmsnrt.rs/2egbfVh
By Helen Reid
LONDON, Oct 2 (Reuters) - Stocks fell worldwide and European assets sold off on Tuesday after anti-euro comments from an Italian lawmaker dented the single currency and sent Italy's bond yields to multi-year highs.
A boost to investors' risk appetite from the new U.S.-Mexico-Canada trade pact proved short-lived with the MSCI world equity index falling back 0.4 percent, its biggest loss in a month.
The leading index of euro zone stocks lost 1 percent and the pan-European STOXX 600 fell 0.7 percent, tracking Asian stocks lower and extending losses as Italian assets came under renewed stress.
U.S. futures also traded down 0.3 percent to 0.4 percent.
Claudio Borghi, the economics spokesman of Italy's ruling League party, 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, falling as much as 2.8 percent and Italy's FTSE MIB tumbled 1.2 percent.
Clarifying his remarks later, Borghi told Reuters that Italy's government has no intention of leaving the euro. However, the spectre of a euro zone breakup and stern words from EU officials about Italy's budget kept markets on edge.
Euro zone banks also dropped 1 percent as the comments reignited investors' anxieties about contagion in the euro zone from Italy's higher-than-expected budget deficit plans, which the government set out on Thursday.
"While our economists do not expect systemic implications for the global economy, contagion risks have risen," Goldman Sachs analysts said.
"We think European risky assets remain vulnerable and there is potential for negative spillovers to the Euro area given the high trade exposure to Italy."
The euro extended losses to fall 0.6 percent to its lowest since Aug. 21 at $1.1504 and was last trading at $1.1509.
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.
"The history of the euro zone tends to be one of great fudges - think of the case of Greece," the Saracen global income and growth fund's manager, David Keir, said.
"But I would caution against any wider systemic spreading. The reality is making kneejerk reactions to big political decisions can very much be the wrong thing to do," he said.
Asian stocks were lower as the lift from an agreement that saved the North American free-trade deal faded.
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 0.4 percent to 95.718, its highest since Sept. 4.
The dollar's strength weighed on the leading emerging markets stock index, which fell 1.5 percent - its biggest one-day loss for a month.
Oil prices recoiled slightly, having hit nearly four-year highs in the previous session.
Crude contracts had surged nearly 3 percent to $75.77 a barrel, their highest since November 2014, as the deal to salvage NAFTA stoked economic growth expectations, with impending U.S. sanctions on Iran seen raising prices.
U.S. crude futures, having touched a high of $75.91, were trading flat at $75.30 a barrel.
Brent crude edged down 0.5 percent to $84.52 a barrel, having rallied the previous day to $85.45, its highest since November 2014.
For Reuters Live Markets blog on European and UK stock markets open a news window on Reuters Eikon by pressing F9 and type in code LIVE/
Reporting by Helen Reid Editing by Louise Ireland