TOKYO, Sept 11 (Reuters) - Japanese shares rose to one-week highs on Friday, tracking U.S. futures higher, after the capital city of Tokyo dropped its coronavirus alert by one notch from the highest level as infections continue to decline.

The benchmark Nikkei share average rose 0.74% to 23,406.49. For the week, the index has gained 0.87%.

The broader Topix gained 0.72% at 1,636.64, with all but four of the 33 sector sub-indexes on the Tokyo exchange trading higher. The index posted its third weekly gain.

Both indexes marked their highest levels since Sept. 3.

Tokyo had raised the alert to "red" in July on the advice of experts following a rise in infections. The city's daily cases have gradually declined since hitting a peak of 472 cases in early August, with 276 new cases reported on Thursday.

Markets had initially opened softer, tracking overnight losses in Wall Street, as heavyweight U.S. tech stocks resumed their decline following a sharp rebound on Wednesday.

But shares recouped losses tracking strength in U.S. futures in Asian trade, with e-mini futures for the S&P 500 adding 0.79% and Nasdaq futures rising about 0.9%.

Shippers were the top performing sector on the main bourse , up 3.16%, with Meiji Shipping Co jumping 5% and Mitsui OSK Lines gaining 3.57%.

Market participants said active buying on special quotation fixing to settle September Nikkei futures and options contributed to the rebound into positive territory.

The market is also awaiting some events next week, including Japan's Liberal Democratic Party leadership election and policy meetings of the Bank of Japan and the U.S. Federal Reserve, said Masahiro Ichikawa, senior strategist at Sumitomo Mitsui DS Asset Management.

Tokyo Dome Corp slipped 1.08% after it forecast a net loss of 18 billion yen ($169.56 million) for the year through Jan. 31, 2021.

($1 = 106.1600 yen)

(Reporting by Eimi Yamamitsu, Editing by Sherry Jacob-Phillips and Amy Caren Daniel)