* GRAPHIC-2020 asset returns: http://tmsnrt.rs/2jvdmXl

* Low LME inventories cap copper's losses

* Copper still close to two-year high

LONDON, Sept 17 (Reuters) - Copper prices were steady in choppy trade on Thursday as high levels of U.S. unemployment took the steam out of a dollar rally a day after an upbeat reading of economic recovery in the world's top economy.

Benchmark copper on the London Metal Exchange (LME) was up 0.1% at $6,786 a tonne by 1727 GMT, having touched a low of $6,676 in the session. This was still close to a two-year high of $6,830 touched on Sept. 1.

Sucden Financial Head of Research Geordie Wilkes said copper was well supported around $6,675 a tonne, adding that following choppy trading overnight some metals had recovered.

Data showing high levels of U.S. weekly jobless claims halted a rally in the dollar that was initially triggered by the U.S. Federal Reserve saying it expects economic growth to improve faster than previously forecast.

Copper and other commodities priced in the dollar are sensitive to its movements. A weaker greenback makes those assets cheaper for non-U.S. firms, a relationship used by funds to generate buy and sell signals.

TRADE: Investment between the United States and China tumbled to a nine-year low in the first half of 2020, hit by bilateral tensions that could pressure more Chinese companies to divest U.S. operations, a research report said.

"U.S.-China tensions will likely have an impact on metals markets going forward and could flare up even more after the U.S election as both candidates have said they want to limit China's influence in the world," Commerzbank's Briesemann said.

STOCKS: On-warrant inventories of copper in LME-registered warehouses were at 46,700 tonnes, near their lowest since March 2019.

The premium for cash copper over the three-month contract was last at $26 a tonne, indicating tight nearby supply.

OTHER METALS: Zinc eased 0.6% to $2,513, snapping a four-session winning streak. Aluminum fell 0.7% to $1,783 a tonne, lead gained 0.3% to $1,901, tin was down 1% to $18,100 and nickel lost 1.1% to $15,065. (Reporting by Zandi Shabalala; Editing by David Goodman and Mark Potter)