TOKYO, May 23 (Reuters) - Japan's Nikkei share average pushed to a fresh 33-year high on Tuesday, helped by a weaker yen and gains for U.S. stock futures amid increased optimism about a debt ceiling deal.

The Nikkei entered the midday break up 0.64% at 31,286.70, putting it on track for a ninth straight winning session, after earlier reaching 31,352.53 for the first time since August 1990.

The broader Topix was 0.38% higher at 2,184.08 after also marking a more than three-decade peak of 2,188.66.

Foreign investors have been the main driver of the Nikkei's rally, drawn by the Tokyo Stock Exchange's (TSE) push for better corporate governance and Warren Buffett's increased investment in some Japanese trading companies.

"Foreign investors are really snapping up Japanese shares at the moment, so the trend higher for the Nikkei is likely to continue," said Masahiro Ichikawa, chief market strategist at Sumitomo Mitsui DS Asset Management.

"At the same time, it's really rallied a long way and there's a strong sense of overheating, so the chance of a correction has become quite pronounced. Investors need to take care about that."

The Nikkei has surged some 7.7% since May 10 to reach Tuesday's high. By contrast, an index of global stocks is up around 0.9% over the same period.

A popular technical indicator called the 14-day relative strength index (RSI) has now topped 85 on a scale to 100. Readings above 70 are generally considered overbought.

Paper and pulp was the top performer among TSE's 33 industry subindexes on Tuesday, gaining 3.3%. Nippon Paper Industries Co leapt 12% to lead Nikkei gainers after Nomura upgraded the stock to "buy".

Other standout winners included Japan Steel Works, which jumped 4.4%, and chip-related stocks including Trend Micro and Renesas Electronics, which gained 4.3% and 3.5%, respectively.

Of the Nikkei's 225 components, 151 rose versus 71 that fell, with three flat. (Reporting by Kevin Buckland; Editing by Shailesh Kuber)