* Canadian dollar hits four-month high, Mexican peso gains
* European stocks follow Japanese higher on trade relief
* Italian budget worries hits bonds, euro
* Chinese manufacturing surveys tempers optimism
* Graphic: World FX rates in 2018 tmsnrt.rs/2egbfVh (Adds turnaround in Italian stocks, adds U.S. stock futures)
By Abhinav Ramnarayan
LONDON, Oct 1 (Reuters) - Optimism about a reconstituted free trade agreement among the United States, Canada and Mexico and what it could mean for trade relations elsewhere helped world markets kick off the fourth quarter of the year in a positive vein.
The United States and Canada salvaged 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 .
Japan's Nikkei rose 0.5 percent to a 27-year high, followed by gains in European stocks markets, with Italian shares in particular clawing back some of last week's losses and U.S. stock futures indicating a sharply higher open on Wall Street.
The Canadian dollar was up 0.85 percent against the dollar to a four-month high and the Mexican peso hit its highest in over seven weeks, up nearly a percent on the day.
"The trade deal is helping risk appetite across the board, especially the Canadian dollar, and that will likely lift appetite for emerging-market currencies across the board," said Manuel Oliveri, a currency strategist at Credit Agricole in London.
A pan-European index of shares was up 0.3 percent, led by Italian stocks, which were up as much as 1.2 percent on the day, bouncing off a two-week low hit last week.
On Friday, Italian stocks, bonds and the euro had all sold off on worries over a budget proposal from Italy's new anti-establishment government, particularly after a report said the European Union was set to reject the plan.
But such were the scale of the losses that some analysts believed the market had gone too far.
"The math just does not justify the price action we saw on Friday. Not even close!" Unicredit economist Erik Nielsen wrote in a note on Sunday.
It wasn't unalloyed optimism on Italy, however, with short-dated bonds selling off with two- and five-year yields higher 7-9 basis points, though there was some demand for longer-dated debt.
The closely watched spread between Italian and German 10-year bond yields was at 268 basis points, about 30 bps wider than this time last week, but comfortably below Friday's high of 278 bps.
"It is quite clear that the European Commission will not like (the budget proposal)," said Commerzbank rates strategist Michael Leister. "Brussels will give its opinion, which we think won't be positive and ... the ratings agencies will opt for a similar stance. A downgrade is our base case."
The euro was also intially hit by worries about a rise in Italy's fiscal deficit, dropping below the $1.16 mark, but it recovered as the session progressed to trade slightly higher at $1.1612.
Also casting a shadow on markets were two surveys on Sunday that showed growth in Chinese manufacturing sputtered in September as domestic and export demand softened.
As a result, MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.25 percent. China's financial markets were closed for a holiday, as was Hong Kong's stock exchange.
"The escalation of trade tensions between the U.S. and China recently has likely weighed on purchasing managers' sentiment as reflected by softer readings in trade-related sub-indices," economists at Bank of America Merrill Lynch said in a note.
Oil prices strengthened with international benchmark Brent hitting a four-year high, as U.S. sanctions on Tehran squeezed Iranian crude exports, tightening supply even as other key exporters increased production.
Brent crude futures rose 0.6 percent to as high as $83.25 per barrel, the highest since November 2014, before trading at $82.98, still comfortably higher on the day. (Reporting by Abhinav Ramnarayan, additional reporting by Hideyuki Sano in Tokyo and Saikat Chatterjee and Virginia Furness in London; editing by Larry King, Richard Balmforth)