The Hang Seng index <.HSI> rose 1.2 percent, to 27,272.39, bringing the week's gain to 7.9 percent.
The China Enterprises Index <.HSCE> gained 1.7 percent, to 13,987.53 points, and produced a weekly gain of 10.5 percent.
On Friday, mainland investors used about half of the 10.5 billion yuan ($1.69 billion) daily quota for Hong Kong shares under the Shanghai-Hong Kong Stock Connect scheme. The quotas were fully taken up on Wednesday and Thursday.
Hong Kong Exchanges and Clearing Ltd (HKEx) (>> Hong Kong Exchanges and Clearing Limited) Chief Executive Charles Li told reporters on Friday that regulatory authorities have been discussing raising the quotas for a while.
"Firstly there definitely will be quota expansion and secondly the expansion will not simply be 20 or 30 percent," Li said.
Among the most actively traded stocks on Hong Kong's main board on Friday were CCT Land (>> CCT Land Holdings Ltd), down 5.3 percent to HK$0.02; GOME (>> GOME Electrical Appliances Holding Ltd.), up 11.5 percent to HK$2.03 and SMIC (>> Semiconductor Manufacturing Int'l), unchanged at HK$0.93.
Total trading volume of companies included in the HSI index was 3.4 billion shares.
(Reporting by Samuel Shen and Pete Sweeney; Editing by Richard Borsuk)