Japan's Nikkei share average rose above the 40,000 mark on Tuesday, hitting a three-month high, as strong overnight gains on Wall Street and a weaker yen boosted sentiment.

The Nikkei index reached 40,257.34 points, its highest level since July 18, after Japanese markets resumed opening after a public holiday yesterday, Monday.

The benchmark index fell in the afternoon to close up 0.8 percent at 39,910.55 points, securing its fourth straight session of gains.

The broader Topix index rose 0.6 percent to close at 2,723.57.

Wall Street closed higher on Monday, with both the S&P 500 and the Dow Jones Industrial Average hitting new record closes.

Nvidia shares rose to a record closing high as semiconductor stocks outperformed others.

That helped lift chip-related shares in Japan, with Tokyo Electron jumping 4.5 percent and Advantest gaining 3.4 percent.

Shares of SoftBank Group, the emerging investment company focused on artificial intelligence, whose subsidiary Arm Holdings jumped 5.8 percent overnight.

LaserTech Corp. rose 6.6 percent, the highest on the index.

Japanese stocks were supported by a weaker yen, which usually boosts exporters' earnings abroad when they repatriate money to Japan.

The yen was close to a low of 149.98 against the dollar on Monday, its lowest since early August.