TOKYO, June 6 (Reuters) - Japan's Nikkei share average rose more than 1% on Thursday, as Tokyo Electron and other chip-related stocks tracked their U.S. peers higher.

The Nikkei was up 1.18% at 38,944.31, as of 0203 GMT, after briefly crossing the 39,000 level earlier in the session.

"Chip shares lifted the Nikkei, but its gains were capped as investors sold stocks as soon as the index crossed a milestone," said Shuutarou Yasuda, a market analyst at Tokai Tokyo Intelligence Laboratory, referring to the 39,000 level.

Chip-making equipment maker Tokyo Electron jumped 4.68% to provide the biggest boost to the Nikkei. Chip-testing equipment maker Advantest jumped 5.22%.

U.S. chip stocks leapt 4.5% overnight, buoyed by gains to Nvidia and Taiwan Semiconductor Manufacturing .

Nvidia's market value hit the $3 trillion mark for the first time as the chipmaker overtook Apple to become the world's second-most valuable company.

"Until the market confirms policy path of central banks in the U.S., Europe and Japan, it will be hard to make active bets on stocks," Yasuda said.

The European Central Bank meets on Thursday, and markets price in an almost certain chance of a first rate cut. The Federal Reserve and the Bank of Japan will hold their policy meetings next week.

The broader Topix was up 0.83% at 2,771.07, with Toyota Motor rising 2.14%.

Of the more than 1,600 stocks traded on the Tokyo Stock Exchange's prime section, 48% rose while 46% fell, with 4% flat.

Technology investor SoftBank Group gained for a second session, rising 3.63% as activist investor Elliott Management has rebuilt a stake worth more than $2 billion and is calling for a $15 billion share buyback. (Reporting by Junko Fujita; Editing by Subhranshu Sahu)