* Euro gains slightly on wobbling U.S. dollar
* Trump warns of govt shutdown over Mexico wall
* Share indices hit by unloved media stocks
* Oil slips on surprise U.S. inventory build
* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh
LONDON, Aug 23 (Reuters) - The European single currency and euro zone government bond yields rose on Wednesday after a survey showed the bloc's manufacturing businesses clocked up their best month of growth in six-and-a-half years.
Forecast-beating surveys in the euro zone's two biggest economies France and Germany helped pull the euro up against the dollar, which had wobbled against the yen overnight on comments from U.S. President Donald Trump.
The pan-European STOXX 600 however, was dragged down by unloved media stocks with WPP shedding more than 10 percent after the world's largest advertising group cut its sales forecast.
"At a broad level what PMIs are telling you is that the momentum of the euro zone recovery continues and the strength of the euro is not containing it," said Investec economist Philip Shaw.
Earlier in Asia, MSCI's broadest index of Asia-Pacific shares outside Japan inched up to a two-week high, before pulling back.
The dollar wobbled against the yen following campaign-rally threats by President Trump to force a government shutdown over funding a border wall.
Financial markets have been buffeted in recent weeks by heightened tensions on the Korean peninsula, turmoil in the White House, and growing doubts about Trump's ability to fulfill his economic agenda.
A gathering of global central bankers this week in Jackson Hole, Wyoming, has prompted investors to rebalance their currency positions, leading them to reduce some of their short dollar bets.
Australian stocks were down 0.3 percent and South Korea's KOSPI gave back earlier modest gains to slip 0.1 percent.
Japan's Nikkei bucked the trend and rose 0.3 percent, lifted as the dollar strengthened against the yen.
The Nikkei took its cues from Wall Street, which saw the Dow rise 0.9 percent, the S&P 500 climb 1 percent and the Nasdaq gain 1.4 percent on Tuesday as technology shares rallied.
The dollar was down slightly against the yen at 109.38 yen by 0900 GMT, back near a day's low plumbed after President Trump told supporters in Arizona "If we have to close down our government, we're building that wall" in reference to his pledge to tighten immigration controls at the U.S.-Mexican border.
The greenback remained clear of a four-month low of 108.605 yen plumbed last week, when turmoil in the White House and geopolitical tensions took a toll on the currency.
The dollar index against a basket of six major currencies was down slightly at 93.409 after rising 0.5 percent the previous day.
The euro was up 0.2 percent at $1.1784 after slipping about 0.5 percent Tuesday on weaker-than-expected German investor confidence.
Speeches from Fed Chair Janet Yellen and European Central Bank President Mario Draghi will headline the annual Jackson Hole event, although neither are expected to announce any significant policy.
In commodities, Brent crude slipped 0.4 percent to $51.64 a barrel after data showed a surprise build in U.S. gasoline inventories. Improving Libyan output also added to oversupply concerns in the crude oil market.
Copper retreated from a three-year high, and other base metals also fell or trimmed gains, as speculators and funds locked in some profits after a steep rally.
Copper on the London Metal Exchange CMCU3 was down 0.2 percent at $6,564 per tonne after striking $6,649 on Tuesday, the highest since November 2014.
Spot gold was a shade higher at $1,286.26 an ounce, after losing 0.5 percent overnight as the precious metal felt the pressure from a stronger dollar. Spot gold had reached a nine-month high above $1,300.00 an ounce on Friday. (Reporting by Ritvik Carvalho in London and Shinichi Saoshiro in Tokyo; Editing by Keith Weir)