* U.S. crude inventories expected to fall for 6th week
* Goldman cuts 2019 oil demand forecast
* GRAPHIC: Iran seizes tanker https://tmsnrt.rs/2O646ZX (Updates prices in paragraph 3)
By Alex Lawler
LONDON, July 23 (Reuters) - Oil slipped to around $63 a barrel on Tuesday as concerns faded for now that rising tensions in the Middle East would escalate and hit oil supplies, compounding the impact of a weaker demand outlook.
Iran's capture of a British oil tanker last week sparked worries about supply disruptions in the Strait of Hormuz, through which about a fifth of the world's oil flows, prompting crude to rally on Monday.
But oil has since pared some gains. Brent crude fell 5 cents to $63.21 a barrel by 1334 GMT on Tuesday.
U.S. West Texas Intermediate crude was up 16 cents at $56.38.
"The response of oil prices to the seizure of a British oil tanker by armed Iranian forces near the Strait of Hormuz has been amazingly muted so far," said Carsten Fritsch, analyst at Commerzbank.
"It appears that the majority of market participants are convinced that there will be no open conflict between the West and Iran," he said.
The tensions come as the United States aims to cut off Iran's oil exports and against the backdrop of supply cuts led by the Organization of the Petroleum Exporting Countries since the start of the year to prop up prices.
As part of U.S. efforts, Washington has imposed sanctions on Chinese state-run energy company Zhuhai Zhenrong Co Ltd for allegedly violating restrictions imposed on Iran's oil sector.
Despite lower Iranian exports and OPEC's voluntary supply curbs, oil supply is exceeding demand due to strong growth in output from the United States and other non-OPEC producers, according to the International Energy Agency.
A weaker outlook for oil demand because of slowing economic growth has weighed on prices, which are still up by 18% in 2019 helped by the OPEC-led supply pact.
"Although prices had been driven by supply developments in the first half of the year economic considerations are making oil bulls careful this month," said Tamas Varga of oil broker PVM.
Goldman Sachs lowered its 2019 oil demand projection on Sunday, joining other forecasters such as the IEA and OPEC in trimming its outlook for fuel use.
Oil may gain further support from expectations of another drop in U.S. crude inventories in weekly reports due later on Tuesday and on Wednesday. Analysts expect a 3.4 million-barrel drop in crude stocks.
The American Petroleum Institute, an industry group, releases its inventory report at 2030 GMT. (Additional reporting by Koustav Samanta; Editing by Susan Fenton and Edmund Blair)
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