A Saudi-led coalition launched a military operation north of Yemen's port city of Hodeidah as the United States worked with Middle East and European nations to build a coalition to deter Iranian threats after the Saudi attack.
Brent crude was up 7.7% since last Friday's close, the biggest weekly rise since January. The front-month November contract was at $64.88 a barrel, up $0.48, by 1113 GMT.
US West Texas Intermediate (WTI) crude futures rose $0.59 to $58.72 a barrel, set to post a gain of over 7% for the week.
"Investors should probably assume that oil stabilises for now in the $60-65 per barrel range, though the risk is to the upside," said Christopher Wood from Jefferies. "The central message from the attacks is the vulnerability of the Saudi infrastructure".
Saudi Arabia's production dropped by almost half after the attack on Saturday, September 14, crippled a major oil processing facility. Its oil minister has pledged to restore lost production by the end of this month.
Reuters reporters were shown repair work under way at Khurais, one of the two attacked sites. Cranes were erected around two burnt-out stabilisation columns, which form part of oil-gas separation units and melted pipes.
Saudi Aramco said at the site on Friday that it was shipping equipment from the United States and Europe to rebuild the damaged facilities.
The United States and Saudi Arabia blame Iran for the assault on Saudi oil facilities. Tehran denies any involvement.
"You have the flooding in Houston as well so going into the weekend, there will be a lot of short covering, which will support prices," Olivier Jakob of Petromatrix consultancy said.
"Next week, you have the UN General Assembly meeting so the focus will turn to whether US President Trump actually meets Iran's president."
In the United States, meanwhile, torrential rain from Tropical Storm Imelda has forced a major refinery to cut production and to shut a key oil pipeline, terminals and a ship channel in Texas.
ExxonMobil Corp shut some units at its 369,024-barrel-per-day (bpd) Beaumont refinery while Valero Energy Corp reduced production at its 335,000bpd Port Arthur refinery.
Global markets were also keeping an eye on US-China trade negotiations in Washington as officials from both sides resumed face-to-face talks for the first time in nearly two months on Thursday.
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