(Fixes typos in paragraphs 13,14)
* Asian stock markets: tmsnrt.rs/2zpUAr4
* Afterglow of US-Mexico relief, firmer China shares support Asia
* Dollar extends gains as rebound in U.S. yields continues
* Crude oil finds some traction after previous day's slide
By Shinichi Saoshiro
TOKYO, June 11 (Reuters) - Asian stocks, led by Chinese shares, gained on Tuesday as markets basked in relief following the U.S. decision to hold off from imposing import tariffs on Mexico as the two governments agreed a deal to combat illegal migration from Central America.
Hopes that U.S. interest rates will be cut as early as next week also provided support.
MSCI's broadest index of Asia-Pacific shares outside Japan gained 0.65%.
The Shanghai Composite Index climbed 1.7% after China said on Monday that it will 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 1.3%, South Korea's KOSPI added 0.3% and Japan's Nikkei edged up 0.35%.
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."
Economists at Societe Generale said in a note that "the probability of the U.S.-China trade conflict drawing to an amicable conclusion has decreased significantly over the past few weeks."
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 96.800 after advancing 0.2% on Monday.
The dollar was up 0.15% at 108.625 yen and the euro was steady at $1.1314 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 experience 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 Fed holds its next policy meeting on June 18-19.
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.
U.S. West Texas Intermediate (WTI) crude oil futures were up 0.36% at $53.45 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)