Brent crude oil held steady above $66 a barrel on Tuesday following the closure of the eastern Libyan oil port of Zueitina by protesters.
Brent crude oil increased 10 cents at $66.55 a barrel, while US crude oil rose five cents to $58.98 a barrel, Reuters reported.
Oil export was still continuing from Zueitina as fighting or disruptions have hampered operations at oil fields hitting export through other ports.
According to officials, oil output in Libya is currently less than 500,000 barrels per day (bpd), which represents a third of what the country pumped prior to the year 2010.
The news agency quoted Commerzbank Frankfurt senior oil analyst saying that after the new rally oil is taking a gulp of air.
Producers of the Organization of the Petroleum Exporting Countries are injecting almost two million bpd that is more than existing demand for their oil, due to which the oil market is supplied adequately.
In June, Organization of Petroleum Exporting Countries (OPEC) ministers are set to meet to discuss production policy.
Strong dollar is also impacting the oil prices as its makes oil dearer for buying in other currencies.
Oil investors are now keenly awaiting inventory data from the US Energy Information Administration which will release its port on Wednesday.