The dollar's strength against the euro is also likely to pressure crude prices downwards, they said.
In morning London trade, New York's main contract, light sweet crude for January delivery, added 60 cents to $84.36 a barrel.
Brent North Sea crude for January gained 43 cents to $86.01 per barrel.
"Oil and the dollar have an inverse relationship so we could see some downward pressure on oil if the dollar continues to rise," said Ong Yi Ling, Phillip Futures' investment analyst.
A stronger dollar makes dollar-priced crude more expensive for buyers using weaker currencies and that in turn tends to hit demand and prices.
"Another factor will be the eurozone debt crisis.... That could affect future demand for oil," she told AFP.
The euro hit a new two-month low on Monday, as Ireland's bailout failed to ease eurozone debt concerns, with the safe-haven greenback also boosted by Korea tensions, dealers said.
In late morning London deals, the single currency plunged to $1.3160, striking the lowest point since September 21.
The European Union and International Monetary Fund agreed Sunday to an 85-billion-euro ($113-billion) deal for Ireland, but the initial boost the announcement gave the euro faded on worries Spain and Portugal could be next in line.
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