New York's main contract, West Texas Intermediate crude for delivery in April, gained 20 cents to $106.78 per barrel while Brent North Sea crude also for April was up 15 cents at $125.59 in morning trade.
Barclays Capital said investors were "buoyed by news that progress was being made on a deal to swap Greek debt, lowering concerns of eurozone economic turmoil."
Positive jobs data from the United States -- the world's biggest economy -- also helped boost prices, it added.
Greece on Thursday appeared to have clinched a high-stakes debt swap, as a deadline for bondholders to accept huge losses on their Greek holdings passed.
According to a government source, participation in the debt-swap operation -- which will erase more than 100 billion euros ($132 billion) in Greek debt -- surpassed 85 percent.
The successful swap will now pave the way for Athens to implement so-called collective action clauses that would force holdouts to accept the deal and unlock a 130-billion-euro ($173 billion) bailout from the European Union and the International Monetary Fund.
The swap would also make repayment of Greece's massive debt, currently at over 350 billion euros, more sustainable in the future, giving its struggling economy much needed breathing room.
Oil prices were also supported by data from the US Department of Labor signalling a fragile recovery in the US jobs market.
Analysts expect further data due to be released later Friday to show that the US economy added a net 206,000 jobs in February, with the unemployment rate remaining unchanged at 8.3 percent from December.