Updates prices as of 0712 GMT

May 7 (Reuters) - London copper prices were largely steady on Thursday, as investors took a breather after the previous session's rally and assessed the prospects of a peace deal between the U.S. and Iran as well as the outlook for the Strait of Hormuz.

Benchmark three-month copper CMCU3 on the London Metal Exchange inched up 0.1% at $13,411 per metric ton by 0712 GMT.

Prices climbed to a near two-week high in the previous session as hopes of easing tensions in the Middle East provided relief to copper, a metal seen as a barometer of macroeconomic health and used widely in power and construction.

The most-traded copper contract on the Shanghai Futures Exchange SCFcv1 rose 0.4% to 102,900 yuan ($15,107.36) per ton.

"The pullback in copper isn't a sign of weakening demand, but rather a 'momentum pause' following Wednesday's rally," said Tim Waterer, chief market analyst at KCM Trade.

"Traders are essentially recalibrating for a world where the Strait of Hormuz isn't permanently blockaded (should a peace deal emerge), and that is allowing for some healthy consolidation at these multi-week highs."

President Donald Trump predicted a swift end to the war with Iran as Tehran considered a U.S. peace proposal that sources said would formally end the conflict while leaving unresolved key U.S. demands that Iran suspend its nuclear programme and reopen the strait.

Oil prices rose about $1 on Thursday, rebounding from the previous day's sharp losses, as investors weighed the prospects of the peace deal succeeding. O/R

Meanwhile, Federal Reserve officials said on Wednesday that the war is raising the risk of a sustained inflation shock, with continued high oil prices and developing concerns about problems with global supply chains.

Among other LME metals, aluminium CMAL3 gained 0.2%, nickel CMNI3 rose 0.4%, lead CMPB3 was up 0.6%, tin CMSN3 gained 1.2% and zinc CMZN3 was up 1.1%.

On the SHFE, aluminium SAFcv1 lost 1.3%, nickel SNIcv1 fell 2.5%, lead SPBcv1 was down 0.3%, zinc SZNcv1 was up 0.8%, while tin SSNcv1 rose 4.1%.