TOKYO, May 16 (Reuters) - Japan's Topix index reached a 33-year high on Tuesday as chip-related stocks tracked overnight gains on the Nasdaq, with sentiment further boosted by optimism that Washington could reach a debt ceiling deal.

By 0210 GMT, the Tokyo Stock Exchange's broader Topix index was up 0.36% to 2,122.55 after hitting 2,126.14, its highest since August 1990.

The Nikkei share average extended gains, jumping 0.62% to 29,810.08, its highest since Nov. 2021.

"The Japanese market was underpinned by momentum on Wall Street today and optimism that the U.S. would make progress on the debt ceiling issue," said Yugo Tsuboi, senior strategist at Daiwa Securities.

"The Nikkei could top 30,000. I say this because it traded 3.6% higher than the 25-day average in the previous session, and in the past the index traded 7% above the average, which means it has more room for gains."

U.S. stocks closed higher on Monday amid flickering optimism that Washington will get past partisan wrangling and reach the debt ceiling deal.

Surging U.S. semiconductor shares boosted the tech-heavy Nasdaq to a solid advance.

Japanese chip-making equipment maker Tokyo Electron Device Ltd jumped 3.71% to lead gains on the Topix and the Nikkei, while chip-testing equipment manufacturer Advantest Corp gained 4.37%.

Recruit Holdings Co Ltd rose 3.3%, boosting the Topix even after the staffing agency posted a decline in its annual profit.

The utility sector rose 1.65% to become the top gainer among the Tokyo Stock Exchange's 33 industry sub-indexes. Retailers rose 1.01%.

Rakuten Group Inc fell 5.44%, extending the previous day's sharp slide after Reuters reported the company would issue new shares to shore up its finances after years of losses from its mobile business. (Reporting by Junko Fujita; Editing by Sonia Cheema)