Oil prices steadied Tuesday after starting the week with losses amid concerns over ample supply and the breakdown in Greece's debt talks.

US benchmark West Texas Intermediate for delivery in July rose 31 cents to $59.83 a barrel compared with Monday's close.

Brent North Sea crude for August was up three cents at $63.98 a barrel London afternoon deals.

"Brent crude oil is trading in a tight range... and the medium-term outlook remains bearish due to the glut of oil that remains on the market," said Kathleen Brooks, research director at traders Forex.com.

Sentiment has been weighed down by worries that US oil output is not declining and Saudi Arabia could further ratchet up production.

Markets are under pressure also owing to Greece's growing problems. Athens and its creditors were locked in a stalemate after loan talks collapsed over the weekend, bringing Greece just two weeks away from a catastrophic default on its debt, which could be followed by its exit from the eurozone.

Both sides have insisted they are willing to engage, but without making a decisive step to break the deadlock.

The talks concerning the release of the 7.2 billion euros ($8.1 billion) in rescue funds remaining in Greece's bailout have dragged on for five months.