* MSCI all-country world stocks index at highest since May 1
* Euro hovers near 2-week highs, yen weakens against dollar
* Coronavirus vaccine trial success sparks rally
* Oil steadies near 2-month high
* Graphic: World FX rates in 2020 http://tmsnrt.rs/2egbfVh
By Marc Jones
LONDON, May 19 (Reuters) - The euro and Italian government bonds continued on Tuesday to cheer German- and French-led plans for a 500 billion euro EU coronavirus recovery fund, though stock markets were suffering from fatigue after their best day in months.
There was still a sense of optimism after Monday's news that early-stage tests on a possible COVID-19 vaccine had also proved encouraging but the momentum was shifting.
Europe's STOXX 600 index .STOXX gave up an early rise to slip 0.4% after surging 4% in the previous session, oil began to tread water O/R and safe-haven U.S. government bonds were making ground in debt markets. GVD/EUR
"The Franco-German proposals are ambitious, targeted and, of course, welcome," European Central Bank President Christine Lagarde said of Monday's plan, which would move the EU in the direction of a so-called 'transfer union'. euro EUR=EBS was buying $1.0932, having gained about 1% against the dollar since the plan was announced. /FRX It was also up near a two-month high against the Swiss franc, while the cost of betting against the euro was falling. a sizeable fall in Italian borrowing costs, Spanish and Portuguese yields led the moves lower on Tuesday. Morgan Stanley (NYSE:MS)'s economists called the Franco-German proposal a "powerful common response, helping to mitigate the risk of a southern slump."
The Spanish 10-year yield fell 9 basis points to 0.715%, the lowest since early April ES10YT=RR , while Portuguese bond yields hit their lowest since March 31, down 12 bps on the day at 0.78% PT10YT=RR .
Italian yields were between 2 and 8 bps lower on the day. The 10-year government bond yield fell nearly 10 basis points to 1.602% IT10YT=RR , its lowest since April 9 at one point.
"It was a meaningful breakthrough but it is not going to be plain sailing from here," said Vasileios Gkionakis, Global Head of FX Strategy at Lombard Odier, citing resistance already voiced by a sizeable number of northern EU countries. the equity markets, Wall Street's S&P 500 futures ESc1 were down 0.4% after Monday's strong rally. .N
Asia had followed. MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS jumped 1.8% to two-week highs and Japan's Nikkei .N225 had added nearly 2%.
In the commodity markets, profit-taking pruned Brent's early gains, though the rally looked broadly intact amid signs that producers are cutting output just as demand picks up. LCOc1 last stood 0.5% higher at $35 a barrel, after touching its highest since April 9. U.S. WTI was at $32.50. Gold was little changed at $1,731 an ounce.
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