* Asian stock markets: https://tmsnrt.rs/2zpUAr4

* Equities shake off slow start to post solid gains

* Investors eye chances for more U.S. stimulus

* Yuan continues recent bull run against dollar

* U.S. presidential election looms large on horizon

By Stanley White and Jessica DiNapoli

TOKYO/NEW YORK, Oct 21 (Reuters) - Asian shares and U.S. stock futures rose on Wednesday as renewed hopes for a new round of U.S. stimulus drew money into equities from government debt.

MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.56%. Australian stocks edged up by 0.1%, while shares in China rose 0.07%. Tokyo shares gained 0.4%.

U.S. stock futures also rose 0.44%.

The yuan surged to the strongest level against the dollar in more than two years on growing optimism about China's economy and speculation that a victory for U.S. Democrat presidential candidate Joe Biden next month will lead to better Sino-U.S. ties.

Benchmark U.S. Treasury yields hit a four-month high and the yield curve steepened on expectations for more U.S. fiscal spending, but some investors remain cautious about the chances of a deal before the U.S. presidential election on Nov. 3.

"It will be quite a mixed day," said Ryan Felsman, senior economist at CommSec. "People are digesting the potential for a stimulus bill, and markets are very cautious on the back of that."

The White House and Democrats in the U.S. Congress moved closer to agreement on a new coronavirus relief package on Tuesday as President Donald Trump said he was willing to accept a large aid bill despite opposition from his own Republican Party.

Negotiations will continue on Wednesday, an aide to top U.S. Democrat Nancy Pelosi said.

On Wall Street, shares of Google parent company Alphabet rose despite an antitrust lawsuit against it by the U.S. Justice Department.

Netflix, however, reported disappointing earnings, leading its shares to fall 6% after trading hours.

The Dow Jones Industrial Average ended up 0.40% on Tuesday. The S&P 500 rose 0.47%, and the tech-heavy Nasdaq Composite rose 0.33%.

The onshore yuan jumped to 6.6602 per dollar, the strongest since July 2018. Yuan bulls have been encouraged by recent signs from the People's Bank of China that it is more comfortable with currency appreciation.

The U.S. dollar hit a one-month low against a basket of major currencies as investors awaited the outcome of the fiscal stimulus talks and as coronavirus cases spiked in Europe.

Benchmark 10-year U.S. Treasury yields hit a four-month high of 0.8060% and the yield curve reached the steepest level in more than four months on hopes lawmakers could agree on a stimulus package.