* Yen, Swiss franc sag after Trump, Xi agree to resume talks

* Offshore yuan at highest levels since early May

* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh (Adds details and quotes)

By Shinichi Saoshiro and Hideyuki Sano

TOKYO, July 1 (Reuters) - The yuan gained and the safe-haven yen slid against the dollar on Monday as appetite for risk-sensitive currencies improved after the United States and China agreed to restart their troubled trade talks.

The dollar rose 0.4% to 108.350 yen, extending its recovery from near a six-month low of 106.78 set last Tuesday.

After meeting Chinese President Xi Jinping in Japan on Saturday on the sidelines of Group of 20 summit, U.S. President Donald Trump said he would hold back on tariffs and that China will buy more farm products.

Trump also said the U.S. Commerce Department would study over the next few days whether to take Huawei off the list of firms banned from buying components and technology from U.S. companies without government approval.

"Most of the discussions that took place between the United States and China at the G20 had already been anticipated, but the mention of Huawei was a bit of a surprise," said Yukio Ishizuki, senior currency strategist at Daiwa Securities.

"There were more dollar short positions than expected, and these are being covered. But once these shorts are covered, the dollar's advance is likely to slow ahead of the non-farm jobs report."

The yen, which attracts demand in times of political tension and market turmoil, also lost ground against other currencies.

The Swiss franc, another safe-haven currency, fell 0.3% to 0.9791 franc to the dollar.

The offshore Chinese yuan gained 0.8% to 6.816 per dollar , its highest levels since May 9, just days after Trump threatened additional tariffs on China.

The euro advanced 0.4% to 123.210 yen and the Australian dollar gained 0.5% to 76.21 yen.

Supported by the greenback's rally against the yen, the dollar index against a basket of six major currencies added 0.15% to 96.280.

The euro was steady at $1.1368 and the Australian dollar was also flat at $0.7027.

The U.S. Treasury 10-year yield was up about 4 basis points at 2.037%, putting some distance between a 2-1/2-year low of 1.974% plumbed on June 20. (Editing by Sandra Maler and Sam Holmes)