* CSI300: +0.2 pct; SSEC: +0.4 pct; HSI: -0.5 pct;
* Markets factor in possibility of a U.S. rate hike in June
* China tells state-owned enterprises to step up restructuring
SHANGHAI, May 19 (Reuters) - China stocks rebounded on Thursday but Hong Kong shares followed other Asian markets lower amid revived concerns of another U.S. interest rate hike as early as June.
China's blue-chip CSI300 index rose 0.2 percent, to 3,075.50 points by lunch break, while the Shanghai Composite Index gained 0.4 percent, to 2,819.42 points.
In Hong Kong, the Hang Seng index dropped 0.5 percent, while the Hong Kong China Enterprises Index lost 0.4 percent.
The markets scrambled to factor in the possibility of another U.S. rate hike soon, after minutes from the last Federal Reserve meeting showed central bank officials felt the U.S. economy could be ready for that in June.
The prospects of further U.S. monetary tightening "would certainly exert pressure on the stock market," said Alex Fan, strategist at GF Holdings (Hong Kong) Corp.
Other uncertainties hurting China and Hong Kong markets include Britain's "Brexit" campaign to leave the EU, and the progress of China's economic restructuring, he added.
Such uncertainty is putting many investors on the sidelines, with trading volume light in both markets.
China markets have been weak recently in light of Beijing's policy shift away from rapid credit expansion to stimulate growth.
In further evidence of that shift, the State Council, or China's cabinet, held a meeting on Wednesday, urging state-owned companies to step up efforts in restructuring and cutting excessive capacity.
But most sectors in China rebounded on Thursday morning after sharp falls during the previous session. Shenzhen's start-up board ChiNext jumped 2.3 percent, recovering much of Wednesday's losses.
In Hong Kong, almost all main sectors fell, with energy shares leading the decline.
Reporting by Samuel Shen and Pete Sweeney; Editing by Richard Borsuk