* Media report says U.S., China have agreed to tentative truce
* Dollar rises as safe havens weaken, yen loses 0.3%
* Euro trades around $1.1365
* Graphic: World FX rates in 2019 tmsnrt.rs/2egbfVh
By Tommy Wilkes
LONDON, June 27 (Reuters) - The dollar extended its recovery on Thursday, gaining versus the yen and euro, on hopes the United States and China will agree a trade truce before a G20 summit in Japan this weekend.
The two countries have agreed to a tentative truce in their trade dispute, Hong Kong's South China Morning Post said, citing sources, before U.S. President Donald Trump and Chinese President Xi Jinping leaders meet on Saturday.
That supported buying of the dollar, which had weakened in recent weeks on expectations the Federal Reserve would cut interest rates and buying of safe-haven currencies such as the Japanese yen by investors worried about the trade conflict.
"The positive signals sent out by the U.S. side in the lead- up to the meeting weaken the `safe havens' JPY and CHF," said Commerzbank analysts, referring to the Japanese yen and Swiss franc.
A dollar index rose 0.1% against a basket of currencies to 96.351. The dollar rose 0.1% against the euro to $1.1356 .
The yen, which had jumped to five-month highs earlier this week, fell 0.3% to 108.10. The Swiss franc dropped 0.2% to 1.1143 francs per euro.
China's offshore yuan rose 0.2% to 6.8778 yuan per dollar , helping the remninbi back towards a six-week high of 6.8370 yuan per dollar touched last week.
The outcome of the Group of 20 summit is expected to influence the Fed, which opened the door to possible rate cuts after last week's meeting.
The potential implications of the Trump-Xi meeting for U.S. monetary policy are huge, said Masafumi Yamamoto, chief forex strategist at Mizuho Securities.
"If the two sides agree not to impose more tariffs, the Fed would no longer need to cut rates," he said. "On the contrary, if the talks point to the imposition of more tariffs, that could nudge hesitant policymakers towards rate cuts.
"Despite the fact that I am not sure whether conciliatory signals ahead of the meeting of the two Presidents really solve all the actual reasons for risk-off."
Elsewhere, sterling fell to $1.2678 as investors wait out the Conservative party leadership contest. Whoever wins will also become Britain's next prime minister and take Britain towards its scheduled departure date from the European Union of Oct. 31. (Additional reporting by Shinichi Saoshiro in Tokyo, editing by Larry King)