LONDON- 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 late last week sparked concern about supply disruptions in the Strait of Hormuz, through which about a fifth of the world's supply flows. Crude rose more than 1% on Monday. 

On Tuesday, Brent crude fell 40 cents to $62.86 a barrel by 1052 GMT. U.S. West Texas Intermediate crude CLc1 slipped 20 cents to $56.02.

"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."

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 that plan, the United States has sanctioned Chinese state-run energy company Zhuhai Zhenrong Co Ltd for allegedly violating restrictions imposed on Iran's oil sector.

But due to strong growth in supply from the United States and other non-OPEC producers, oil supply is exceeding demand, according to the International Energy Agency, despite lower Iranian exports and OPEC's voluntary supply curbs.

A weaker outlook for oil demand due to 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 on Sunday lowered its 2019 oil demand projection, 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 Louise Heavens and Susan Fenton) ((alex.lawler@thomsonreuters.com; +44 207 542 4087; Reuters Messaging: alex.lawler.reuters.com@reuters.net))