Shares in China remained under pressure after falling by more than 5% on Friday when it was revealed that the country`s top brokerages were being investigated.
The Shanghai Composite fell 3% at first, but recovered some ground later to close up 0.26% at 3,445.4 points.
A wave of new share listings this week is also expected to weigh on the Chinese market.
In Hong Kong, the benchmark Hang Seng index closed down 0.33% at 21,996.42 points.
"A renewed selloff in mainland Chinese markets have heightened fears that Friday`s selloff could merely be the beginning of a more significant correction for Chinese equities," said IG market analyst Angus Nicholson.
The Shanghai market saw its biggest one-day drop in more than three months on Friday.
Investors will be looking at manufacturing surveys for November, due later this week, for signs of slowing growth in the world`s second-largest economy.
No boost from Japanese data
Positive economic data from Japan failed to inspire investors. Japan`s factory output rose 1.4% in October from a month ago, marking the second consecutive monthly rise, although the figure fell short of forecasts.
However, economists at research firm Capital Economics said the second monthly rise in industrial production following two months of contraction suggested the economy returned to growth in the fourth quarter.
"In particular, the rebound in core capital goods shipments last month suggests that business investment should start to recover this quarter," Japan economist Marcel Thieliant said.
Retail sales grew more than expected, up 1.1% from a month ago.
Despite that, Japan`s Nikkei 225 index finished down 0.7% at 19,747.47.
The rest of Asian shares were also lower, with investors looking ahead to US jobs data and the European Central Bank meeting later this week for trading cues.
In Australia, the S&P/ASX 200 index closed down 0.7% at 5,177.50. Shares in BHP Billiton fell 3.6% on fears over the costs of the dam at the Samarco iron ore mine.
BHP, which jointly-owns Samarco with Vale, said it was expecting the Brazilian government to begin legal action against the two companies demanding about $5.2bn for "environmental recovery and compensation".
Shares in electronics retailer Dick Smith plunged as much as 70% at one point after it said it would take a 60m Australian dollar ($43m; £28m) impairment on inventories after disappointing sales. The firm`s shares ended down 58%.
South Korea`s benchmark Kospi index closed down 1.8% at 1,991.97 after data showed industrial output posted a surprise decline in October.
Factory output fell by a seasonally adjusted 1.4% from September, marking the fastest drop since May.
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