* Asian stock markets: tmsnrt.rs/2zpUAr4
* European stock futures touch higher in early trade
* U.S.-Mexico relief, firmer China shares support Asia
* Dollar extends gains as rebound in U.S. yields continues
* Crude oil finds traction after previous day's slide
By Shinichi Saoshiro
TOKYO, June 11 (Reuters) - Asian stocks gained on Tuesday, led by Chinese shares after Beijing eased financing rules to boost local government spending on public works, and bolstered by investor relief following a U.S. decision to hold off import tariffs on Mexico.
Hopes that U.S. interest rates will be cut as early as next week have also provided broader support.
In early European trade, the pan-region Euro Stoxx 50 futures were up 0.06%, German DAX futures gained 0.04% and FTSE futures added 0.14%.
MSCI's broadest index of Asia-Pacific shares outside Japan gained 0.8%.
The Shanghai Composite Index climbed 2% after China said on Monday that it would allow local governments to use proceeds from special bonds as capital for major investment projects in a bid to support the slowing economy.
Australian stocks rose 1.5%, South Korea's KOSPI added 0.55% and Japan's Nikkei edged up 0.3%.
U.S. stocks extended their recent climb on Monday, with the Dow rising for the sixth trading day.
Relief that the United States had stepped back from an immediate imposition of tariffs on Mexico encouraged buyers, though U.S. Secretary of State Mike Pompeo warned the United States could still slap tariffs on Mexico if not enough progress was made on its commitment to stem illegal immigration.
While global markets have been given some reprieve, fresh U.S. trade threats against China were seen limiting any major boost to investor sentiment.
U.S. President Donald Trump said on Monday he was ready to impose another round of punitive tariffs on Chinese imports if he cannot make progress in trade talks with Chinese President Xi Jinping at the G20 summit.
The U.S. president has repeatedly said he expected to meet Xi at the June 28-29 summit in Osaka, Japan, although China is yet to confirm any such meeting.
"The lift from the U.S.-Mexico trade development is likely to be a temporary one for the equity markets as the bigger issue between the United States and China remains unresolved," said Masahiro Ichikawa, senior strategist at Sumitomo Mitsui DS Asset Management.
"Nervousness will prevail in the markets until the G20 summit. And there is no guarantee that matters will improve even if the U.S. and Chinese leaders meet at the summit."
Tensions between Washington and Beijing rose sharply in May after the Trump administration accused China of having reneged on promises to make structural economic changes during months of trade talks.
Investors worry that the conflict could prompt China to retaliate by putting U.S. companies on a blacklist or banning exports to the United States of rare earth metals. China accounts for roughly 80% of U.S. rare earths supply which are essential for high-tech goods.
Rare earth production: tmsnrt.rs/2I9MfL5
In the currency markets, the dollar extended gains it made against its peers in the wake of Friday's agreement between the United States and Mexico.
The dollar index against a basket of six major currencies was a shade higher at 96.774 after advancing 0.2% on Monday.
The dollar was up 0.15% at 108.600 yen and the euro was steady at $1.1315 following a loss of 0.2% the previous day.
The benchmark U.S. Treasury 10-year yield stretched an overnight spike and touched an 11-day peak of 2.157%. The yield had risen about 6 basis points on Monday as the U.S.-Mexico deal boosted risk appetite and curbed investor demand for safe-haven government debt.
The Treasury market has experienced volatility over the past week, with the 10-year yield having fallen to a near two-year low of 2.053% on Friday after a soft U.S. jobs report raised expectations for an interest rate cut by the Federal Reserve.
The prospect of the central bank lowering rates this year had already risen earlier last week after a number of Fed officials including Chairman Jerome Powell hinted they were open to easing monetary policy.
Market focus was on the Fed's next policy meeting on June 18-19 and what kind of signals the central bank could use to provide regarding monetary policy direction.
"While it easy to focus on the potential reaction should the Fed not meet the market pricing, a world where the Fed signals an intent to ease married with a better feel to U.S.-Sino relations, is a world where traders take additional risk," wrote Chris Weston, Melbourne-based head of research at foreign exchange brokerage Pepperstone.
U.S. West Texas Intermediate (WTI) crude oil futures were up 0.58% at $53.57 per barrel, finding some traction after sliding the previous day.
Crude oil fell on Monday, with U.S. futures losing 1.3%, as major producers Saudi Arabia and Russia had yet to agree on extending an output-cutting deal and with U.S.-China trade tensions continuing to threaten demand for the commodity. (Editing by Simon Cameron-Moore and Sam Holmes)