* MSCI Asia-Pacific index up 0.1 pct, Nikkei gains 0.3 pct
* Korean, Japanese stocks gain
* Chinese stocks volatile on MSCI inclusion day
* U.S. slaps tariffs on Canadian, Mexican and EU aluminium & steel
* U.S. tariff moves reignite global trade conflict woes
By Shinichi Saoshiro
TOKYO, June 1 (Reuters) - Asian equities shook off earlier weakness on Friday, as a softer yen supported Japanese stocks and firm export data drove South Korean markets higher, although rekindled concerns about U.S. protectionist trade policies limited gains.
MSCI's broadest index of Asia-Pacific shares outside Japan gained 0.1 percent but the index was still down roughly 0.6 percent for a week in which it touched a six-week low on concerns about political developments in Italy.
Wall Street shares posted deep losses overnight after the United States said it would impose tariffs on aluminium and steel imports from Canada, Mexico and the European Union.
Fears of a global trade conflict, which had partially receded over the past few weeks, were reignited as Washington's allies took steps to retaliate against the U.S. measures.
However, regional sentiment recovered somewhat with South Korea's KOSPI up 0.7 percent on upbeat export data while Japan's Nikkei advanced 0.3 percent, buoyed by the yen's weakening against the dollar.
More broadly, Soichiro Monji, senior economist at Daiwa SB Investments in Tokyo, expected equity markets to be weighed down "as the United States has opened up a new point of contention on the trade front by getting involved with the European Union."
"President (Donald) Trump has not accomplished very much in terms of trade issues and is likely to remain vocal with the U.S. midterm elections coming up," he said.
In China, stocks were volatile, with the long-awaited inclusion of big cap shares from the country in MSCI's emerging markets index failing to buoy the market or attract any immediate flows of foreign money.
The Shanghai Composite Index fell 0.3 percent and the blue-chip CSI300 index dropped 0.55 percent.
On Friday, about 230 yuan-denominated mainland A-shares were included in MSCI's emerging markets index for the first time in a step toward deeper integration of China's bourses with the rest of the world.
Bank of America Merrill Lynch estimates that at full inclusion, China's A-shares could account for some 30 percent of MSCI's emerging market index.
"It took Korea and Taiwan some six to nine years to gain full weighting. It may take (China's) A-shares longer in our view due to size, access and capital mobility constraints," wrote equity strategists at Bank of America Merrill Lynch.
In currencies, the Canadian dollar and the Mexican peso were on the defensive, weighed by the U.S. decision to impose tariffs on aluminium and steel imports from these countries.
The euro was little changed at $1.1696 holding to modest gains made on relief overnight as Italy's anti-establishment parties reached a deal to resurrect their proposed coalition government.
The deal by the Italian parties averted the prospect of a new snap election, which had rattled global markets earlier this week and sent the euro to a 10-month low of $1.1510 on Tuesday.
The dollar climbed 0.4 percent to 109.240 yen. It has lost about 0.1 percent against the yen this week as the earlier global market tumult had enhanced demand for the Japanese currency, which is a perceived safe-haven.
Brent crude dipped 0.1 percent to $77.50 a barrel.
Prices swerved between $$74.49, a three-week low, to $78.75 this week on speculation towards output by major oil-producing nations.
U.S. crude was down 0.15 percent at $66.94 a barrel.
Brent's premium over U.S. crude reached its widest since March 2015 this week as a lack of pipeline capacity in the United States has trapped a lot of output inland.
Editing by Sam Holmes