(Refiles to remove extra word in first paragraph)
* CSI300 +0.6, SSEC +0.3, HSI +1 pct
* Headed for modest weekly gain
* Supported by stimulus hopes but technically overbought
By Sue-Lin Wong
SHANGHAI, Jan 9 (Reuters) - China stocks edged up on Friday and looked set to post modest gains over a volatile week, but investors were wary that a near-term correction may be looming after a sharp run-up in the last few weeks.
The CSI300 index rose 0.6 percent to 3,578.72 points, while the Shanghai Composite Index gained 0.3 percent to 3,301.63 points, keeping them in overbought territory on technical charts.
For the week, they looked set for gains of 1.2 percent and 2.1 percent, respectively, a relatively mild pace compared with their surge in past weeks.
"After yesterday's tumble, we are still seeing energy and banks backing down but the scope of the back down won't be that great," said Liu Jingde, an analyst at Cinda Securities.
The bank sub-index was down 0.1 percent, with Agricultural Bank of China down 1.1 percent and Construction Bank of China down 0.9 percent. Brokerages were mostly mixed.
Offsetting losses in banks were infrastructure shares which rose 1.6 percent.
After gaining around 40 percent in the fourth quarter of last year on hopes that Beijing will roll out more stimulus measures for the cooling economy, the market opened 2015 on a strong note, rising over 3 percent on Monday.
However, sentiment cooled after the securities regulator approved 20 initial public offering late on Monday, around double the monthly average it allowed last year, which was taken as a sign that authorities will allow more supply into the market this year.
In Hong Kong, the Hang Seng index added 1.0 percent to 24,081.75 points, heading for a weekly gain of 0.9 percent.
The Hong Kong China Enterprises Index gained 1.7 percent to 12,221.68.
The index measuring price differences between dual-listed companies in Shanghai and Hong Kong stood at 126.77.
A value above 100 indicates Shanghai shares are pricing at a premium to shares in the same company trading in Hong Kong, and vice versa.
Total volume of A shares traded in Shanghai was 16.93 billion shares, while Shenzhen volume was 7.93 billion shares.
Total trading volume of companies included in the HSI index was 1.0 billion shares.
New A-share account openings bit.ly/1wvJ9S9
China trading volumes hit records in 2014 link.reuters.com/vag73w
Editing by Kim Coghill