* SSEC 0.2%, CSI300 0.3%, HSI 0.4%
* HK->Shanghai Connect daily quota used 1.3%, Shanghai->HK daily quota used 1.4%
* FTSE China A50 +0.3%
SHANGHAI, Dec 20(Reuters) - China and Hong Kong stocks firmed on Friday, heading for their third straight weekly gain on improving relations between Washington and Beijing after they reached an initial trade deal last week.
** The Shanghai Composite Index rose 0.2% to 3,022.90 at the end of the morning session, having gained 1.9% so far this week. The CSI300 index advanced 0.3% to 4,039.49.
** The Hang Seng index added 0.4% to 27,902.68 and was up 0.8% for the week. The Hong Kong China Enterprises Index firmed 0.5% to 11,044.92.
** U.S. Treasury Secretary Steven Mnuchin said on Thursday the United States and China would sign their so-called Phase one trade pact at the beginning of January, adding that it was completely finished and just undergoing a technical "scrub."
** China on Thursday unveiled a new list of import tariff exemptions for six chemical and oil products from the United States, days after the world's two largest economies announced a Phase 1 trade deal.
** As the initial trade deal removed some of the uncertainty over the Sino-U.S. tariff dispute, investors turned their focus to the health of the world's largest economy and Beijing's policy moves.
** China's economy could face more downward pressure in 2020 than it did this year, but the government will take steps to keep growth within a reasonable range, state television on Thursday quoted Premier Li Keqiang as saying.
** Economic growth slowed to near 30-year lows in the third quarter, however, policymakers have been more cautious about growth boosting measures than in past downturns.
** China stood pat on its lending benchmark rate on Friday, as widely expected, after the central bank kept borrowing costs of medium-term loans steady earlier this month.
** Around the region, MSCI's Asia ex-Japan stock index was firmer by 0.06%, while Japan's Nikkei index was up 0.03%.
** The yuan was quoted at 7.008 per U.S. dollar, 0.03% firmer than the previous close of 7.01.
* So far this year, the Shanghai stock index is up 20.98%, while China's H-share index is up 8.5%. Shanghai stocks have risen 5.05% this month.
** As of 0410 GMT, China's A-shares were trading at a premium of 26.85% over the Hong Kong-listed H-shares. (Reporting by Luoyan Liu and John Ruwitch; Editing by Aditya Soni)