Analysts said the weather was being monitored. Royal Dutch Shell removed about 360 workers from the region over the weekend as a precaution.
US light, sweet crude fell 42 cents to $113.35 a barrel while London Brent crude lost 46 cents cents to $112.09.
The dollar weakening slightly also supported oil prices, observers said.
In addition, supply worries lifted the oil price - which had fallen to as low as $111 on Friday.
BP said that exports of Azeri oil by rail to Georgia had stopped because of "damage" to a railway line caused during the military conflict between Russia and Georgia.
Softer demand
The euro and pound both strengthened slightly against the dollar on Monday after the greenback had enjoyed a strong rally last week.
The falling dollar tends to push oil prices up as investors buy into crude and other commodities as a hedge against inflation.
Oil prices are still well off the peak of $147 a barrel hit in July.
Last week's forecast by the Opec cartel of oil producing nations that demand would grow more slowly than previously thought in 2008 and 2009 also helped to prevent prices from rising .