Benchmark crude for March delivery was up 30 cents at $87.03 a barrel at midday Singapore time in electronic trading on the New York Mercantile Exchange. The contract rose 2 cents to settle at $86.73 on Thursday.
In London, Brent crude gained 49 cents to $101.93 a barrel on the ICE Futures exchange.
Mubarak said late Thursday that he would pass some authority to his vice president but would not immediately leave office. Protesters seeking to oust Mubarak said they would hold a massive rally later Friday in Cairo.
Egypt is not a major oil producing country, but it controls the Suez Canal and a nearby pipeline. Egypt's political crisis, which is entering its 18th day, hasn't disrupted oil supplies, but traders are concerned the upheaval could spread to other countries in the oil-rich region.
"There are renewed fears that the events in Egypt will be copied elsewhere throughout the Middle East," Cameron Hanover said in a report. "The possibility of other countries in the region coming under similar assaults seems to grow."
In other Nymex trading in March contracts, heating oil rose 1 cent to $2.72 a gallon and gasoline gained 1.7 cents to $2.49 a gallon. Natural gas futures for March delivery were down 2.2 cents at $3.96 per 1,000 cubic feet.