Oil prices rebounded on Tuesday as Iran and six major powers extended a deadline for reaching a nuclear deal that could add Iranian oil to an oversupplied global market.

US benchmark West Texas Intermediate (WTI) for delivery in August rose $1.14 to $59.47 a barrel.

In London, Brent North Sea crude for August closed at $63.59 a barrel, an increase of $1.58 from Monday's settlement.

Both key futures contracts had fallen on Monday as Greece lurched toward a debt default and potential exit from the eurozone. The uncertainty roiled markets, pushing WTI down $1.30 and Brent $1.25.

Traders focused on Iran nuclear talks in Vienna for a deal to end the 13-year standoff between Iran and six major powers over Tehran's controversial program.

Iran and the so-called P5+1 -- the United States, Britain, China, France, Russia and Germany -- gave themselves an extra week, until July 7, to clinch an agreement after no breakthrough in the negotiations was in sight ahead of a midnight deadline Tuesday.

Under the framework of the talks, Iran agreed to substantially scale down its nuclear activities in order to make any attempt to develop nuclear weapons -- an aim denied by Tehran -- virtually impossible.

In return, sanctions that have suffocated the Iranian economy by choking its lifeblood oil exports will be progressively lifted.

"For the oil market the Iran nuclear deal is fundamentally most important even though Greek turmoil will help to throw the oil market around from day to day," said Bjarne Schieldrop, chief analyst at Commodities SEB Markets.