(Reuters) - News of North Korean leader Kim Jong-il's death accelerated falls on Monday for Hong Kong and China shares, but they later pared some of the losses and outperformed most regional peers.

In Hong Kong, the index came up later in the day because short positions were covered, while in Shanghai it was bargain-hunting on beat-down stocks that trimmed the day's losses.

The Hang Seng Index ended down 1.2 percent at 18,070.2 points, offsetting the bulk of Friday's gains, while the China Enterprises Index of the top mainland listings in Hong Kong slipped 1.4 percent.

The Shanghai Composite Index closed down 0.3 percent at 2,218.24, bouncing off a 33-month intraday low.

Turnover was lacklustre in both Hong Kong and Shanghai.

The markets opened lower, before Kim's death was announced, because of ongoing worries about Europe and disappointment that China has not made any policy easing moves to follow up a Nov. 30 cut in bank reserve requirements. On Friday, speculation that China would be doing more pushed up share prices.

Risk reduction is still the main theme. Europe is still the main focus for investors for now, said Benjamin Chang, chief executive officer of LBN Advisors, which manages $450 million of assets in two China funds.

After the Hong Kong and Shanghai markets closed Friday, Fitch Ratings warned it may downgrade France and six other euro zone countries, saying a comprehensive solution to the region's debt crisis was technically and politically beyond reach.

Chang said he does not expect uncertainty about North Korea to impact Hong Kong and China markets too adversely, with much depending on events in the next few days.

Chinese property and financial counters, which led gains on Friday largely on a bout of short-covering, were the leading percentage losers on Monday.

Data over the weekend showed that China's November housing prices increased at the slowest rate this year while housing inflation was the lowest as tightening efforts took affect.

Chinese insurer PICC Property & Casualty Co Ltd slumped 6 percent in relatively strong volume, while China Resources Land Ltd lost 4 percent.

Chinese shipper, Cosco Pacific Ltd was the one of the top losers among Hang Seng Index components, declining 5.1 percent to the lowest in more than two months in relatively strong volume. It is down almost 38 percent in 2011, poised for its worst year since 2008.

CAN SHANGHAI SEE A REBOUND?

Some market watchers contended that Shanghai's 33-month intraday low could serve as a base for a short-term rebound.

But they were not optimistic the bounce up would sustain, with data on Monday showing that China recorded a second month of capital outflows in four years in November as a slowing domestic economy and mounting global uncertainties led some investors to withdraw speculative funds.

In the afternoon's bargain-hunting in Shanghai, Ping An Insurance, China's second-largest insurer, reversed early losses to end up 0.5 percent. It is still down more than 35 percent in 2011.

Chinese insurers are seen as barometers of the mainland A-share market because of their high levels of investments. China Life Insurance, Ping An's larger rival, was down by as much as 5.2 percent at midday, but closed off 3.2 percent.

Chongqing Brewery Co Ltd slumped by the daily maximum of 10 percent for an eighth straight session, to the lowest since September 2010. It has lost more than 52 percent since resuming trading on Dec. 8 after an eight-day suspension.

Local media reported that securities regulators could launch an investigation into alleged insider trading relating to the free fall in Chongqing Brewery's share price.