TOKYO, Nov 6 (Reuters) - Japan's Nikkei share average closed at a more than one-month high on Monday, tracking a Wall Street rally in the previous session, with chip-related stocks leading the charge.

The Nikkei index jumped 2.37% to 32,708.48, its highest closing level since Sept. 20. The broader Topix rose 1.64% to 2,360.46.

Wall Street's main stock indexes rallied on Friday as bond yields fell sharply after data showed signs of slowing U.S. jobs growth and an uptick in unemployment, boosting hopes that the Federal Reserve is done with its interest rate hiking campaign.

"Wall Street was firm at the end of last week after weaker-than-expected economic data, which prompted investors to scoop up Japanese stocks," said Shuutarou Yasuda, market analyst at Tokai Tokyo Research Institute.

"The next step is to see whether the Nikkei will cross the 33,000 level in the short term," Yasuda said, adding the subdued U.S. data shows the economy may be slowing down, which could weigh on Japanese equities.

The U.S. Labor Department's report showed nonfarm payrolls increased by 150,000 jobs in October, much less than the expected 180,000 increase.

In Japan, chip-testing equipment maker Advantest jumped 8.15% to give the biggest boost to the Nikkei. Chip-testing equipment maker Tokyo Electron rose 2.14%.

Uniqlo-brand owner Fast Retailing rose 1.58% and staffing agency Recruit Holdings jumped 7.43%.

Sanrio surged 7.28% after the owner of the Hello Kitty character raised its annual profit forecast.

Kawasaki Kisen fell 11.38% after the shipping firm cut its annual profit forecast.

The index for shipping firms declined 5.21% to become the worst performer among the 33 industry sub-indexes on the Tokyo Stock Exchange.

The banking sector slipped 2.06%.

(Reporting by Junko Fujita; Editing by Rashmi Aich and Sonia Cheema)