Recasts, updates prices and changes dateline to London

By Alex Lawler

LONDON, June 29 (Reuters) - Oil prices steadied on Monday as Iran and the United States agreed to halt recent hostilities in the Gulf and Middle East producers pushed ahead with loading oil and liquefied natural gas despite fresh ship attacks.

The two countries also agreed to renew talks over the Strait of Hormuz, raising hopes of saving an interim peace deal that had been threatened by days of tit-for-tat strikes.

Brent crude futures LCOc1 were up 4 cents at $72.03 a barrel by 0803 GMT. U.S. West Texas Intermediate crude CLc1 gained 44 cents, or 0.6%, to $69.67.

"There's still plenty of risk facing the oil market. Even so, participants appear to be ... focusing on what a continued recovery in oil flows would mean for the global balance," ING analysts said in a note on Monday.

"This complacency is odd and clearly leaves significant upside risk if the supply recovery proves slow."

Brent crude fell 10.6% last week for a third consecutive weekly decline after crude shipments through the strait rose last week to their highest since the U.S.-Israeli war on Iran began in late February.

Middle East producers are pushing ahead with loading oil and LNG despite fresh ship attacks in the Strait of Hormuz and renewed strikes between the U.S. and Iran in recent days, shipping data showed.

Saudi oil giant Aramco 2222.SE resumed crude oil loadings on Friday at its Ras Tanura terminal, west of the Strait of Hormuz, after they were halted for nearly four months.

Loadings continued even after a helicopter belonging to the company crashed on Sunday at Ras Tanura, killing 14 nationals. The cause of the crash was unknown.