By early afternoon in Europe, benchmark West Texas Intermediate crude for July delivery was up 97 cents to US$91.83 a barrel in electronic trading on the New York Mercantile Exchange. The contract rose 20 cents to settle at $90.86 in New York on Friday.
In London, Brent crude for July delivery was up 96 cents at US$107.79 a barrel on the ICE Futures exchange.
Opinion polls published Sunday indicated two parties that favour implementing Greece's bailout programs may be able to form a coalition government. Greek politicians were unable to form a government after an election earlier this month, requiring new elections in June.
Crude has dropped from US$106 the first week of May amid fears a chaotic Greek exit from the euro would deepen economic malaise and weaken crude demand in Europe.
Easing tensions over Iran's nuclear program amid talks between Iran and six world powers have also helped lower oil prices, but analysts warned that it is too early to dismiss the risk factors on that front.
Iran and the international powers "remain as far apart as ever," according to energy consultants KBC in London. "So the situation remains clouded and the negotiators' position a tricky one. Inevitably the issue will run right down to the wire."
Some analysts expect oil will linger near current prices until after the Greek vote, OPEC's quarterly meeting and the next round of Iran nuclear discussions in mid-June.
"Both European debt and Iranian nuclear issues are on something of a hold for another month," Barclays said in a report. "We would not expect the oil market to gain much of a sustained sense of direction" before those events.
Markets are in the U.S. were closed Monday for the Memorial Day holiday.
In other energy trading, heating oil was up 1.53 cents at US$2.8482 a U.S. gallon (3.79 litres) and gasoline futures added 2.39 cents to US$2.8556 per gallon. Natural gas fell 7.1 cents to US$2.556 per 1,000 cubic feet.
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