* Asian stocks edge lower as short-covering has run its course
* Bond yields under pressure globally
* UK bond yields, pound under pressure on BoE remarks
* Asian stock markets: tmsnrt.rs/2zpUAr4
By Hideyuki Sano and Stanley White
TOKYO, July 3 (Reuters) - Asian shares fell on Wednesday as initial enthusiasm over the latest U.S.-China trade truce was overtaken by fresh concerns over Washington's threat of tariffs on additional European goods.
Global growth concerns also weighed on investor confidence, with South Korea the latest trade-reliant economy to cut its economic growth and export targets, a day after weaker factory readings worldwide.
MSCI's broadest index of Asia-Pacific shares outside Japan was 0.3% lower, while Japan's Nikkei slipped 0.6% in early trade.
U.S. stocks managed modest gains on Tuesday after holding near the unchanged mark for much of the session, with the S&P 500 gaining 0.29% to a record close of 2,972.98, underpinned by dividend-oriented utilities and real estate stocks.
Still, a rally in global stocks following the U.S.-China summit at weekend is rapidly losing steam. While the threat of new U.S. tariffs has been postponed for now, existing tariffs that have disrupted global supply chains are unlikely to be lifted any time soon.
The United States and China agreed on Saturday to restart trade talks after President Donald Trump offered concessions including no new tariffs and an easing of restrictions on tech company Huawei in order to reduce tensions with Beijing.
"The easing of Huawei ban was a bit of surprise so there was a bit of short-covering. But there remain questions over how effective the agreement will be," said Norihiro Fujito, chief investment strategist at Mitsubishi UFJ Morgan Stanley Securities.
Data published so far this week has showed factory activity in the euro zone shrank at a faster pace than expected last month and U.S. manufacturing activity slowed in June. Most Asian factory gauges also contracted.
Moreover, the U.S. Trade Representative's office released a list of additional European products that could be subject to tariffs, on top of products worth $21 billion that were announced in April. These included olives, Italian cheese and Scotch whisky.
Global bond yields are also hitting new lows as investors bet on further monetary easing around the world amid faltering global growth.
Bank of England Governor Mark Carney on Tuesday flagged uncertainties stemming from trade disputes and Britain's departure from the European Union even as he stuck to his line that the central bank could raise rates in the event of a smooth Brexit.
The UK gilts yield tumbled 9 basis points to 0.722 , the first time in a decade the 10-year yield is below the BOE's main policy rate.
European bond yields are expected to fall further after European Union leaders agreed late on Tuesday to name France's Christine Lagarde as the new head of the European Central Bank. .
In the United States, Trump said on Tuesday he intends to nominate Judy Shelton, an economic adviser to his 2016 presidential campaign, and Christopher Waller, an executive vice president at the Federal Reserve Bank of St. Louis, to the Federal Reserve board of governors.
"Lagarde is likely to follow current ECB President Mario Draghi's dovish stance," said Norio Miyagawa, senior economist at Mizuho Securities.
"Trump has made it very clear he would prefer the Fed cut rates, so I am sure he will try to lead it in that direction. However, the International Monetary Fund has warned about the risks of easing over an extended period because this depresses yields so much."
The 10-year yield fell below two percent to go as low as 1.969%, a low last seen in November 2016.
In the currency market the pound flirted with two-week lows after Carney's comments and last stood at $1.2599.
The euro was steadier at $1.1291 while the dollar traded at 107.87 yen, off Monday's high of 108.535 hit after China and the United States agreed to resume trade talks.
Oil prices rose a tad after data showed U.S. crude inventories fell more than expected last week but remained wobbly after four-percent dives on Tuesday even after OPEC and allies including Russia agreed to extend supply cuts until next March.
Brent crude futures traded at $62.85 per barrel, up 0.7% after having fallen 4.1% on Tuesday.
U.S. West Texas Intermediate (WTI) crude futures rose 0.6% to %56.56 a barrel, following 4.8% drop the previous day. (Editing by Kim Coghill & Shri Navaratnam)