Oil prices steadied on Tuesday as traders eyed the possible return of Iranian crude to the global market with supplies already at high levels, analysts said.

The market was responding also to movements in the euro against the dollar, and how that affects demand for dollar-denominated crude oil, awaiting a deal on Greece's bailout terms.

Iran and major Western powers are racing to agree a deal by June 30 that would see Tehran open up its nuclear programme to allay concerns it is seeking atomic weapons, in return for the West lifting punishing economic sanctions.

Any agreement could result in Iranian crude returning to the world market, adding to the current oversupply which sent prices plunging from more than $100 a barrel last year.

In Tuesday trade, US benchmark West Texas Intermediate for August delivery was down 23 cents at $60.15 a barrel compared with Monday's close.

Brent North Sea crude for August edged up eight cents to $63.42 a barrel in London midday deals.

Oil prices had risen modestly on Monday amid hopes of there finally being a breakthrough on Greece's financial rescue.

Elsewhere is the key issue of "Iranian crude possibly coming back to the market", said Daniel Ang, an investment analyst with Phillip Futures in Singapore.

He said market-watchers are concerned over how fast Iran can resume exports to the West after a deal is reached.

"If the speed is very fast, this could push the market into further oversupply," he said.

Iran and the so-called P5+1 powers -- Britain, China, France, Germany, Russia and the United States -- had agreed in April on the main outlines of what would be a historic deal scaling down Tehran's nuclear programme.

In return, they agreed that sanctions would be progressively lifted if regular inspections confirm that Tehran is sticking to the accord.