Benchmark crude for January delivery was down 78 cents to $92.75 a barrel at midday Singapore time in electronic trading on the New York Mercantile Exchange. The contract fell 34 cents to settle at $93.53 on Friday.
In London, Brent crude was down 45 cents at $102.90 on the ICE futures exchange.
Asian stock markets dropped Monday amid fears Kim's death could lead to greater instability on the divided Korean peninsular. South Korea's stock market fell 3.3 percent, Hong Kong slid 2.5 percent and Japan was down 1.1 percent.
Crude has fallen from above $100 earlier this month on growing fears Europe's debt crisis will trigger a recession on the continent next year and undermine global oil demand.
Oil prices have been supported by signs of a slowly improving U.S. economy, and the latest data on U.S. housing and gross domestic product are scheduled to be announced later this week.
"Attention to these numbers could shift focus away from Europe for a week or so and toward the U.S. with a potential rebound in the stock market sparking another rally across the energy complex," energy consultant Ritterbusch and Associates said in a report.
In other energy trading on the Nymex, natural gas fell 4.0 cents to $3.09 per 1,000 cubic feet. Heating oil dropped 1.3 cents to $2.80 a gallon and gasoline futures were down 1 cent to $2.49 a gallon.
