TOKYO, Oct 2 (Reuters) - Japan's Nikkei share average erased earlier gains to end lower on Monday as investors sold stocks amid worries about rising interest rates.

The Nikkei index fell 0.31% to close at 31,759.88, after jumping as much as 1.7% earlier in the session.

The broader Topix changed course to end 0.39% lower at 2,314.44.

"The Japanese equities rose after a positive outcome of the Bank of Japan's (BOJ) business survey. Investors bought stocks also as they were relieved that the U.S. government avoided a federal shutdown," said Shuutarou Yasuda, a market analyst at Tokai Tokyo Research Institute.

The central bank survey showed big non-manufacturers' mood brightened in the third quarter to levels unseen since 1991, when Japan was experiencing an asset-inflation bubble, while companies retained their robust spending plans and faced a tight labour market.

The U.S. Congress late on Saturday passed a stopgap funding bill with overwhelming Democratic support in a bid to avoid the federal government's fourth partial shutdown in a decade.

"But investors realised the overall situation has not been changed because yields on Japanese government bonds kept rising, which weakened stocks last week," Yasuda said.

Japanese government bond yields across the curve kept rising on Monday, with the 10-year bond yields hitting a fresh high since September 2013. That prompted the BOJ to announce additional bond buying.

Chip-making equipment maker Tokyo Electron fell 1.27% to drag the Nikkei the most. Technology start-up investor SoftBank Group lost 1.34%.

The banking index jumped 1.24% to become the top performer among the 33 industry sub-indexes on the Tokyo Stock Exchange.

(Reporting by Junko Fujita; Editing by Rashmi Aich)