TOKYO, Sept 8 (Reuters) - Japan's Nikkei share average hit a one-week high on Thursday, tracking Wall Street's overnight strong finish, with the yen's fall to a 24-year low against the dollar raising hopes for better outlook for domestic firms.

By 0217 GMT, the Nikkei jumped 2.1% to 27,996.26, before crossing the key psychological 28,000-mark for the first time since Aug. 31.

The broader Topix had advanced 1.94% to 1,952.81, after falling for six consecutive sessions.

The dollar surged to a 24-year peak against the yen overnight, as Japan's dovish monetary policy contrasted with a hawkish Federal Reserve.

"Weakening yen is basically good for Japanese exporters and that could boost their earnings per shares," said Shuji Hosoi, senior strategist at Daiwa Securities.

"The rebound of the Nasdaq index after a seven-session losing session has boosted sentiment for Japanese equities market."

Hosoi also said the gain in Japanese equities is temporary because the gap in rates in Japan and the United States is set to widen, limiting the yen's potential for gains against the dollar.

Chip making equipment maker Tokyo Electron rose 2.31% and gave the biggest boost to the Nikkei, followed by Uniqlo clothing shop owner Fast Retailing, gaining 1.61%.

Air-conditioning maker Daikin Industries rose 3% and techno investor SoftBank Group rose 2.27%.

Airlines was the top gainer among the Tokyo Stock Exchange's 33 industry sub-indexes, rising 3.47%, as Japan further relaxed its infection border controls.

ANA Holdings and Japan Airlines advanced 3.04% and 4%, respectively.

Department stores were also strong, with Isetan Mitsukoshi and J.Front Retailing climbing 2.92% and 2.98%, respectively.

Park24 lost 5.39%, after Tokyo prosecutors raided the headquarters of the parking services firm in connection to Tokyo 2020 Olympic bribery investigations. (Reporting by Junko Fujita; Editing by Rashmi Aich)