New York's main contract, West Texas Intermediate crude for delivery in April, gained 40 cents to $105.10 per barrel while Brent North Sea crude for April delivery was up 50 cents at $122.48.
Israeli Prime Minister Benjamin Netanyahu ended a visit to the United States on Tuesday with assurances that Washington is prepared to use force to prevent Iran from getting a nuclear weapon.
Netanyahu, who met President Barack Obama and Secretary of State Hillary Clinton during the visit, put the world on notice that his patience was wearing thin and, if necessary, he would launch unilateral strikes.
Iran has denied it is building an atomic bomb, saying its nuclear programme is for peaceful purposes.
Security analysts say a nuclear-armed Iran would alter the balance of power in the politically volatile Middle East.
"Concerns over Iran's nuclear ambitions are... a factor (for the price rise), despite signs that Iran is willing to return to talks," said Nick Trevethan, senior commodities strategist at ANZ Research.
EU foreign policy chief Catherine Ashton offered Tuesday to resume talks between global powers and Iran in response to Iran's chief negotiator Saeed Jalili's call for negotiations to be resumed at the "earliest" opportunity.
Iran has previously threatened to close the strategic Strait of Hormuz -- a transit point for one-fifth of the world's oil supply -- if the West imposes further sanctions.