New York's main contract, light sweet crude for delivery in January, closed at $93.88 a barrel, an increase of 35 cents from Friday.
The futures contract, which had lost about $6 last week, rebounded slightly Monday despite lackluster financial markets.
In London, Brent North Sea crude for February delivery climbed 29 cents to settle at $103.64 a barrel.
"The concerns about the Korean peninsula and Iran are helping to stabilize prices," said John Kilduff at Again Capital.
"Other than that there is not a lot of news and not a lot of participation, so it is a relatively quiet day," he said.
North Korea's Kim Jong-Il, 69, died of a heart attack Saturday, state media announced on Monday, baring new questions about the future of the nuclear-armed and deeply isolated communist nation.
Pyongyang urged support for Kim's youngest son Kim Jong-Un, who is in his late 20s and was last year made a four-star general and given top ruling party posts despite having had no public profile.
Phil Flynn at PFG Best pointed to Fitch Ratings downgrades on six major global banks last Thursday that heightened fears over the eurozone debt crisis.
"Oil traders as well as other markets are running for cover as the hope that Europe might get tidied up looks less likely," he said.
Meanwhile, unprecedented deadly riots in oil-rich Kazakhstan forced the government Saturday to declare a 20-day state of emergency in the Caspian town of Zhanaozen.
In other developments, cash-strapped Sudan said Monday it would open six exploration blocks for bidding by international oil companies on January 15, after losing 75 per cent of its oil production when the south separated in July.
The vast majority of Khartoum's export earnings came from the now-divided country's production of 470,000 barrels per day of crude, leaving the government now scrambling for ways to bolster its finances.
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