SHANGHAI, Jan 9 (Reuters) - China and Hong Kong stocks tracked broader Asian markets in a relief rally on Thursday as the United States and Iran backed away from the brink of further conflict in the Middle East.
** Investors also drew optimism from data showing China's December factory-gate price deflation eased, adding to signs of modest improvement in manufacturing activity and factory profitability.
** The CSI300 index was up 0.8% at 4,145.69 points, at the end of the morning session, while the Shanghai Composite Index gained 0.5% to 3,081.36 points.
** The Hang Seng index added 1.1% to 28,386.93 points, while the Hong Kong China Enterprises Index gained 1.2% to 11,214.59.
** China stocks dropped the most in two weeks on Wednesday, after Iran's firing of missiles at U.S.-led forces in Iraq stoked fears of a wider conflict in the Middle East.
** U.S. President Donald Trump responded overnight the Iranian attack with sanctions, not violence. Iran offered no immediate signal it would retaliate further over a Jan. 3 strike by the United States that killed one of its senior military commanders.
** Also aiding sentiment was easing factory-gate price deflation that suggest Beijing's stimulus measures might have helped to steady the economy.
** The producer price index (PPI), seen as a key indicator of corporate profitability, fell 0.5% from a year earlier. Analysts had expected factory-gate prices to fall 0.4% on-year, compared with a 1.4% drop in November.
** Consumer price pressures, notably for food, also appeared to have eased. The consumer price index (CPI) in December rose at a pace unchanged from November - an eight-year high of 4.5% - but was less than expected.
** China's CSI300 financial sector sub-index was trading 0.62% higher, the consumer staples sector rose 0.77%, the real estate index climbed 1.7% and the healthcare sub-index advanced 1.99%.
** The smaller Shenzhen index was up 1.03% and the start-up board ChiNext Composite index was higher by 1.75%.
** Around the region, MSCI's Asia ex-Japan stock index was firmer by 1.09%, while Japan's Nikkei index climbed 2.02%.
** In Hong Kong, the sub-index of the Hang Seng index tracking energy shares dipped 0.4%, while the IT sector rose 1.6%. The top gainer in the Hang Seng was Hengan International Group Co Ltd, up 5.73%, while the biggest decliner was PetroChina Co Ltd, which was down 1.45%. (Reporting by Samuel Shen and Brenda Goh, Editing by Sherry Jacob-Phillips)