* Asian stock markets: tmsnrt.rs/2zpUAr4
* Shares ex-Japan recoup last week's losses
* U.S. officials continue to sound optimistic on trade
* Pro-democracy candidates sweep to power in HK vote
* Dollar benefits as U.S. economy outperforms
By Wayne Cole
SYDNEY, Nov 25 (Reuters) - Asian shares staged a cautious rally on Monday as investors dared to hope for some progress in the endless Sino-U.S. trade dispute, while the outperformance of recent U.S. economic data gave the dollar a leg up on its peers.
MSCI's broadest index of Asia-Pacific shares outside Japan bounced 0.7%, after losing 0.4% last week.
Japan's Nikkei firmed 0.7%, while Australian stocks rose 0.5% and Shanghai blue chips 0.3%.
E-Mini futures for the S&P 500 added 0.2%, while EUROSTOXX 50 futures gained 0.6%. FTSE futures firmed 0.3%.
On Saturday, U.S. national security adviser Robert O'Brien said an initial trade agreement with China is still possible by the end of the year, though he warned Washington would not turn a blind eye to what happens in Hong Kong.
The comments add to worries that a Chinese crackdown on anti-government protests in Hong Kong could further complicate the talks.
Over the weekend, pro-democracy candidates in Hong Kong romped to a landslide and symbolic majority in district council elections in the embattled city.
"The fact that talks are still happening remains a positive," said Robert Rennie, head of financial market strategy at Westpac. "Markets are showing some signs of tiring of the steady drip feed of upbeat comments from U.S. officials and no signs of a final agreement looking likely."
He noted six weeks had passed since the "phase one" deal was agreed in principle yet there was still no deal in place.
"Key for markets will thus be whether the Dec. 15 tariffs covering approximately $156 billion of largely technology imports are postponed and whether a deal can be signed ahead of that date, with press suggesting that these tariffs will be delayed to give negotiators more time."
Reuters reported an ambitious "phase two" trade deal was also looking less likely, according to U.S. and Beijing officials, lawmakers and trade experts.
In currency markets, the dollar had rallied on Friday when U.S. manufacturing surveys beat forecasts, just as European Union numbers disappointed.
"U.S. economic data outperformed, highlighting again the resilience of the economy and that while global growth has slowed, it remains the least dirty t-shirt in the laundry basket," said Tapas Strickland, a director of economics and markets at National Australia Bank.
"For the EU data, the important takeaway was the ongoing decline in the manufacturing sector is now spreading to the larger services sector, a worrying sign for the global economy."
European Central Bank President Christine Lagarde on Friday called on euro zone governments to strengthen domestic demand after a global trade war brought a decade of export-driven growth to an abrupt end.
Federal Reserve Chair Jerome Powell speaks later on Monday and is expected to underline the steady outlook for rates given the better economic figures.
The euro was off at $1.1020 on Monday, having breached chart support at $1.1040, while the dollar edged up to 108.76 yen.
The dollar was steady on a basket of currencies at 98.271 , after gaining 0.3% last week.
Spot gold was flat at $1,461.20 per ounce, restrained by the bounce in the dollar.
Oil prices held near two-month highs helped by expectations of an extension to OPEC+ production cuts.
Brent crude futures firmed 17 cents to $63.58, while U.S. crude rose 13 cents to $57.90 a barrel.
Editing by Sam Holmes