* Market relieved after China shares rise * Toshiba underperforms on ongoing false accounting woes By Ayai Tomisawa TOKYO, July 13 (Reuters) - Japan's Nikkei share average rose on Monday morning after sharp rallies in U.S. shares encouraged investors to buy stocks on dips, but the market stayed wary of developments in Greece.

The Nikkei share average rose 0.9 percent to 19,960.50 in mid-morning trade after falling 3.7 percent last week. On Monday, the index was still 1.6 percent below its 25-day moving average of 20,284.84.

Chinese shares, which opened higher, also supported market sentiment. In China, the Shanghai Composite index and the CSI300 index of China's biggest-listed companies were up 2.0 percent and 1.7 percent, respectively at 0136 GMT.

Analysts said investors were in an anxious mood, with many market-related events likely to dominate trading this week.

U.S. Federal Reserve Chair Janet Yellen testifies on the economy before Congress on Wednesday while a slew of U.S. earnings are slated this week as well.

"It's hard to predict this week's moves because the market is likely to be swayed by individual events," said Hikaru Sato, a senior technical analyst at Daiwa Securities. "When the Nikkei recovers its 25-day moving average there will be more sense of relief. For now, investors are still cautious." Investors will continue to focus on developments in Europe.

Euro zone leaders argued late into the night on Sunday with near-bankrupt Greece at an emergency summit, demanding Athens enact key reforms this week to restore trust before they will open talks on a financial rescue to keep it in the European currency area.

Exporters were in demand, with Toyota Motor Corp rising 1.9 percent, Honda Motor Co gaining 1.0 percent and Tokyo Electron Ltd adding 1.1 percent.

Underperforming the market was Toshiba Corp, which earlier dipped more than 3 percent to a 2-1/2-year low on ongoing false accounting woes.

Kyodo news reported over the weekend that Toshiba President Hisao Tanaka was expected to step down to take responsibility for accounting irregularities, citing sources. Toshiba was not immediately available for comments when contacted by Reuters.

The broader Topix rose 1.3 percent to 1,604.20 and the JPX-Nikkei Index 400 advanced 1.2 percent to 14,487.32.

(Editing by Jacqueline Wong)