* Better-than-expected China imports helps dollar off session lows

* Sterling steadies after volatile swings ahead of Brexit vote

By Lisa Twaronite and Shinichi Saoshiro

TOKYO, June 8 (Reuters) - The dollar plumbed a fresh four-week trough against a basket of currencies on Wednesday, though better-than-expected Chinese import figures helped it climb off session lows.

The dollar index, which tracks the greenback against a basket of six rivals, edged down 0.1 percent to 93.740 after dropping as low as 93.695, its lowest since May 11.

Against its Japanese counterpart, the dollar slipped 0.3 percent to 107.05 yen , after hitting a session low of 106.72 earlier. It remained off the one-month low of 106.35 touched on Monday but still a long way away from levels above 111 yen at the end of May.

Underpinning risk appetite and helping the dollar climb off its lows against the perceived safe-haven yen, data showed that China's imports beat forecasts in May, adding to hopes that the economy may be stabilising even though exports fell more than expected.

"Stocks rose after the China trade figures, in a bit of a 'risk on' reaction, because imports didn't fall as much as expected," said Ayako Sera, market strategist at Sumitomo Mitsui Trust Bank in Tokyo.

"The data had an impact on stocks, which did have some effect on forex, but ahead of next week's Fed meeting, it's difficult to have an extreme 'risk on' or 'risk off' move in either direction," she said.

The euro rose 0.2 percent to $1.1373 . It had closed the last two days virtually flat after its 2 percent surge on Friday's disappointing U.S. non-farm payrolls report that all but quashed expectations for a Federal Reserve interest rate hike this month.

"A June U.S. rate hike is now out of the question and the focus is whether the Fed provides any hints of a July hike. There are no major U.S. indicators until the Fed's policy meeting next week, and the dollar is likely to remain bearish until then," said Junichi Ishikawa, forex analyst at IG Securities in Tokyo.

The Fed concludes a two-day policy meeting on June 15.

The dollar got a small lift overnight after revised figures on U.S. productivity and labour costs in the first quarter supported the view that labour market slack is being gradually reduced.

The Australian dollar edged up 0.1 percent to $0.7462 after surging more than 1 percent in the previous session to a one-month high of $0.7465 following the Reserve Bank of Australia's decision to stand pat on monetary policy and hint it was not in a hurry to raise rates.

Elsewhere, the speculation over whether Britain will vote to remain in the European Union at a referendum on June 23 continued to sway the pound.

Sterling was steady at $1.4551 after having gained roughly 0.8 percent overnight as two polls gave a narrow lead to the "Remain" camp.

The New Zealand dollar added 0.3 percent to $0.6999 after scaling a one-month peak of $0.7006 earlier.

The Reserve Bank of New Zealand is scheduled to announce its policy decision early on Thursday, with the market expecting the central bank to keep monetary policy unchanged.

(Editing by Jacqueline Wong; Editing by Simon Cameron-Moore) ((lisa.twaronite@thomsonreuters.com;)(+81 3 6441 1870; Reuters Messaging:)(lisa.twaronite.thomsonreuters.com@reuters.net))