Markets began the day on a low after Belgium's credit rating was cut, France's outlook was lowered and six other eurozone members were put on downgrade watch.
Tokyo fell 0.84 percent by the break, Hong Kong was two percent lower, Sydney tumbled 2.39 percent and Shanghai gave up 2.21 percent.
Seoul was down more than four percent.
North Korean state television said 69-year-old Kim died on Saturday and that the country must now follow his son Kim Jong-Un. Stock markets slipped further soon after the announcement as dealers become nervous about the future direction of the nuclear-armed communist country.
On Friday, Moody's Investors Service cut Belgium's credit rating by two notches, citing tough conditions for in-debt European countries to borrow with little chance of a quick end to the eurozone crisis.
The agency reduced Brussels' rating to Aa3, with a negative outlook, from Aa1.
Fitch Ratings lowered its outlook on France's triple-A rating to negative from stable, saying the debt crisis "constitutes a significant negative shock to the region and to France's economy and the stability of its financial sector".
The agency also placed six eurozone nations, including Spain and Italy, on watch for downgrade, saying it considered a "comprehensive solution" to the crisis was technically and politically beyond reach.
Hiroichi Nishi, general manager of the equity division at SMBC Nikko Securities, told Dow Jones Newswires: "Downgrades don't really surprise us these days, but they will still weigh on sentiment."
The dire warnings from the ratings agencies came ahead of a European finance ministers' teleconference on Monday that will aim to fill in details of this month's debt-fighting agreement.
The talks, which will include non-euro members, will also discuss boosting International Monetary Fund (IMF) coffers to enable it to come to the aid of floundering economies.
At the recent summit, which saw Britain block plans for EU treaty change to save the currency, member countries announced plans to pump 200 billion euros ($260 billion) into an IMF warchest.
On currency markets the euro bought $1.3035 and 101.43 yen in early Asian trade Monday, compared with $1.3032 and 101.37 yen in New York late Friday.
The dollar was also flat against the Japanese currency, trading at 77.81 yen.
New York's main contract, light sweet crude for delivery in January, fell 43 cents to $93.10 a barrel while Brent North Sea crude for February shed 55 cents to $102.80.
Gold was trading at $1,593.20 an ounce at 0200 GMT, against $1,590.95 an ounce late Monday.