TOKYO — Japan’s key Nikkei stock index surged more than 3% on Thursday to end at a two-week closing high, as a weaker yen benefited exporter shares and strong Asian stocks gave an additional boost to a market that had been battered by eurozone debt woes. The 225-issue Nikkei Stock Average rose 310.95 points from Wednesday to 9,914.19, the highest closing level since May 20 when it ended at 10,030.31. The Topix index of all First Section issues on the Tokyo Stock Exchange gained 20.59 points to 890.64. After an overnight jump on Wall Street initially boosted sentiment, a softer yen against the euro and the dollar and the strong performances of Asian stock markets added to the momentum for picking up shares, brokers said. The yen has weakened amid market speculation that Finance Minister Naoto Kan, who has said he favors a weaker yen for the economy, will replace Prime Minister Yukio Hatoyama following his decision on Wednesday to step down. ‘‘Stocks had been seen as reasonable to buy after going through an adjustment phase (that sent them sharply lower recently),’’ said Hideaki Higashi, assistant manager at SMBC Friend Securities Co. ‘‘The euro’s slide seems to be taking a respite for now…and I think the market is trying to decide whether to go back to economic data (for trading cues) and to see what the next scenario would be’’ after eurozone woes took center stage, Higashi added.

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