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* GRAPHIC: World FX rates in 2019 http://tmsnrt.rs/2egbfVh
TOKYO, June 11 (Reuters) - The yen eased on Tuesday as investors' risk appetite ticked up after the United States shelved plans to impose tariffs on Mexico, though fresh U.S. trade threats against China tempered overall market sentiment.
Financial markets over the last year have been gripped by fears of escalating trade tensions between the world's two largest economies, stoking worries over the outlook for global growth.
Against the safe-haven yen, the dollar advanced nearly 0.2% to 108.625 yen, extending a similar gain during the previous session.
The dollar index, which measures the greenback against a basket of six peers, edged up 0.05% to 96.799, building on a 0.2% gain achieved overnight.
U.S. President Donald Trump said on Monday he was ready to impose another round of tariffs on Chinese imports if he does not reach a trade deal with China's president at the Group of 20 summit in Osaka, Japan near the end of the month.
Since two days of talks to settle the U.S.-China trade dispute last month in Washington ended in a stalemate, Trump has repeatedly said he expected to meet Chinese President Xi Jinping at the G20 gathering. China has not confirmed any such meeting.
"It might not happen if the Chinese side thinks there isn't any point in having a meeting if the opinions are far apart from the start," said Yukio Ishizuki, senior currency strategist at Daiwa Securities.
"Trump has been applying pressure by emphasising there will surely be a meeting, but it isn't clear what the Chinese side will do."
Broader market sentiment got a lift from the U.S.-Mexico trade and migration deal, sending U.S. government bond yields higher overnight.
Futures for the S&P 500 were last up 0.2%, recovering after trading in negative territory early in the session. U.S. 10-year Treasury bond yields hit their highest since May 31 .
"The avoidance of tariffs on Mexican goods are supporting risk sentiment," said Masafumi Yamamoto, chief currency strategist at Mizuho Securities.
Investors were hesitant to take on more risk because of "uncertainty" about what Trump does in relation to China ahead of the G20 summit, he said.
In offshore trade, the Chinese yuan was last up 0.2% at 6.9310 yuan per dollar, reversing an early loss. It was still hovering not far off a near seven-month low brushed on Friday.
Elsewhere, the Australian dollar was largely steady at $0.6961, recovering after dipping to a one-week low earlier in the session.
The euro was little changed at $1.1314.
The single currency dipped on Monday after two sources familiar with the European Central Bank's policy discussions said on the weekend that a rate cut was firmly in play if the bloc's economy stagnates again after expanding by 0.4% in the first quarter.
The euro rallied nearly 1.5% last week after the ECB said rates would stay "at their present levels" until mid-2020 instead of hinting at rate cuts, as some had expected.
(Reporting by Danial Leussink Editing by Joseph Radford & Shri Navaratnam)