* Graphic: World FX rates in 2018 tmsnrt.rs/2egbfVh
* MSCI ACWI hits highest since March 13
* Dollar slips as trade worries ebb
* Oil prices edge higher
By Ritvik Carvalho
LONDON, Sept 21 (Reuters) - World shares hit their highest levels in more than six months on Friday as investors took the view that the latest exchange of tariffs between the United States and China may be less damaging than initially feared.
European stocks strongly extended a relief rally that began on Wall Street overnight and ran through Asian markets, with the pan-European STOXX 600 index up 0.4 percent by 1223 GMT. Futures indicated a higher open on Wall Street .
A rally in Chinese markets helped lift the MSCI's broadest index of Asia-Pacific shares outside Japan 1.27 percent, partly on expectations that Beijing will pump more money into its economy to weather the trade war. The index has risen 4.6 percent from a 14-month low on Sept. 12.
The CSI 300 index of Shanghai and Shenzen shares, which fell to a two-year low last week, rose 3 percent, putting it on course for its largest weekly gain for more than two years.
Japan's Nikkei rose 0.8 percent, hitting an eight-month high.
The broad strength across markets helped MSCI's All-Country World Index, which tracks shares in 47 countries, hit its highest level since March 13. The index was last up 0.4 percent on the day, and was set to post its biggest weekly gain since early May.
On Wall Street, trade-sensitive industrial stocks led the gains on Thursday. The Dow Jones Industrial Average rose 0.95 percent while the S&P 500 gained 0.78 percent, both hitting record highs.
The latest rally came after new U.S. and Chinese tariffs on each other's goods were set at lower rates this week than previously expected, raising hopes that row between the world's two largest economies may be easing.
Chinese Premier Li Keqiang pledged this week that Beijing will not engage in competitive currency devaluation, news that also helped calm investors.
"The tariffs that were announced by both sides during the week were deemed to be not as harsh as originally suspected," CMC Markets markets analyst David Madden said.
"The U.S. in particular showed restraint, but that was partially so the Trump administration would have more ammunition should they feel it is required down the line. Now that the latest series of tariffs are out of the way, investors fell back into their bullish routine."
Despite growing anecdotal reports from companies on both sides of the Pacific that the trade war is starting to affect their operations, the outlook for corporate profits remained solid in many markets on the back of strong global growth, keeping equity valuations relatively attractive.
Still, some analysts warned that the reversals in various assets including U.S. industrial shares and non-U.S. developed markets might be driven primarily by position-squaring before the end of the quarter rather than reflecting a decisive shift in sentiment.
In the currency markets, the dollar turned positive on the day after slipping to a two-month low against a basket of major currencies as worries eased over the trade row.
The euro last traded at $1.1767, easing slightly on the day after touching a 3-month high of $1.18030 after a euro zone manufacturing survey came in below forecasts.
"The weakness in the dollar is prompting investors to unwind their short bets against other currencies such as the euro and this move may have further room to run," Credit Agricole currency strategist Manuel Oliveri said.
The closely watched summit of the European Union and the United Kingdom produced little progress on the thorny issues of trade and the Irish border.
Britain's former Brexit minister David Davis has said up to 40 lawmakers from the ruling party will vote against Prime Minister Theresa May's plans to leave the bloc, meaning she may struggle to get her exit deal through parliament.
The pound last stood at $1.3228, down 0.3 percent on the day .
Amid positive risk sentiment, the yen slid to a two-month low of 112.88 to the dollar. Oil prices rose ahead of a meeting of OPEC and other large crude exporters that will focus on production increases as U.S. sanctions restrict Iranian exports.
In Europe on Friday, U.S. light crude was up 0.7 percent at $70.82 a barrel. Brent crude oil rose 1 percent to $79.53 a barrel.
Spot gold rose 0.1 percent to $1,208.93 an ounce.
Reporting by Ritvik Carvalho Additional reporting by Saikat Chatterjee in London and Hideyuki Sano in Tokyo Editing by Louise Ireland