* CSI300 index +3.6 pct, Shanghai Composite +2.7 pct
* Trump said to want trade agreement with Xi at G20
* Domestic investors cheer Xi support pledge for private firms
* .HSI up 4.2 pct, biggest daily percentage rise since late 2011 (Updates with Hong Kong closer figures, milestones and comments)
By Andrew Galbraith and Noah Sin
SHANGHAI/HONG KONG, Nov 2 (Reuters) - Shares in China and Hong Kong shot higher on Friday, propelled by a report that U.S. President Donald Trump is seeking a trade agreement with Chinese President Xi Jinping.
Investors were also cheered by Xi’s pledge on Thursday of government support for private businesses, which are facing severe strains as the Chinese economy slows.
The blue-chip CSI300 index ended up 3.6 percent at 3,290.25 points, taking its gains for the week to 3.67 percent. The Shanghai Composite index ended 2.7 percent higher at 2,676.48, and was up 3 percent for the week.
However, both indexes remain well in the red for the year. The CSI300 has lost 18.5 percent and the Shanghai Composite is down 19.1 percent, pulled down by worries about the impact of the Sino-U.S. trade row on corporate profits and economic growth.
Consumer staples firms posted particularly strong gains, with the sector index rising 6.2 percent.
Distiller Kweichow Moutai Co gained 6.6 percent on Friday after a string of volatile sessions and a weak earnings report that left it down 1.7 percent for the week.
The financial sector sub-index added 2.7 percent, real estate firms rose 0.4 percent and the healthcare sub-index closed 5.3 percent higher.
The smaller Shenzhen index ended up 3.4 percent and the start-up board ChiNext Composite index rose 4.8 percent, with smaller enterprises getting a boost from a promise of private sector support from Xi, who pledged more tax cuts and financial aid.
“This is part of a series of encouragements coming through from the government,” said Zhang Qi, an analyst at Haitong Securities in Shanghai, referring to policy support announced by regulators, such as enhanced market liquidity, earlier this week.
Shares had posted solid gains in the morning session, and extended the rally after the midday break on a Bloomberg report that Trump is interested in reaching a trade agreement with Xi at the G20 summit in Argentina later this month, and has asked key U.S. officials to begin drafting potential terms.
The report came after the two leaders expressed optimism about resolving their trade disputes following a phone call.
Uncertainty over global trade has been one of the major factors behind the recent equity market rout, with recent economic data pointing to a deepening global impact from the trade war.
“Trump’s announcement of positive trade war developments comes just days before the midterm elections, and its momentous impact reveals the delicate state of investor sentiment,” said Robert Olivar, partner at O&G Capital Management in Shanghai.
In Hong Kong, the main Hang Seng index recorded its biggest daily percentage rise since December 2011, closing up 4.2 percent at 26,486.35.
The Hang Seng rose 7.2 percent this week, its highest weekly percentage gain since April 2015.
The index for Chinese companies in Hong Kong was up nearly 4 percent on Friday.
A confluence of factors, inspired by easing trade tensions, drove the local market higher, said Ben Kwong, director of research at KGI Asia in Hong Kong.
“The renminbi is stronger today, that is the dominating factor,” he said. “Hong Kong stocks have also been down for 6 months now, people are hoping for a technical rebound this month.”
The offshore yuan firmed 6.8955 per dollar in afternoon trade, the first time it has traded at a level stronger than 6.90 to the dollar since Oct. 12.
At 0716 GMT, the offshore yuan was trading at 6.8848 per dollar.
The onshore yuan touched 6.9083, and was at 6.8889 at 0716 GMT, on track for its first weekly gain in six weeks.
Chinese government bond futures fell. The 10-year Treasury bonds for December delivery, the most traded contract, were 0.47 percent lower at 95.500.
Around the region, MSCI’s Asia ex-Japan stock index was firmer by 2.85 percent, while Japan’s Nikkei index closed up 2.56 percent.
“We have had a lot of negative headlines for a long time, with the trade war going on and the renminbi weakening,” said Zhang at Haitong Securities.
With both these factors turning around, “confidence is on the rise in China.” (Reporting by Andrew Galbraith and Noah Sin Editing by Shri Navaratnam and Kim Coghill)