Roads and Transport Authority has been working round the clock to carry out maintenance work
Concerns about OPEC producer Iran's nuclear programme also underpinned the market.
US light crude was trading 20 cents lower at $124.90 by 1112 GMT, while London Brent crude rose 14 cents to $124.32.
Prices have recovered from a low hit last week of $120.42, the weakest since early May and far below the record of $147.27 struck on July 11.
They reached a session high of $126.35 early on Monday before easing slightly after a Reuters survey showed OPEC supply had risen for a third consecutive month in July mainly because of increased output from the world's top exporter Saudi Arabia.
The modestly bearish impact was countered by Tropical Storm Edouard, which formed near a major oil and gas producing area of the northern Gulf of Mexico on Sunday, the US National Hurricane Center said.
‘The market still looks firm, although it is down from highs,’ a broker said. ‘Iran and Edouard are the main points to keep an eye on.’
The storm was expected to come ashore at close to hurricane strength in a few days on the Texas coast.
Oil firms, including Royal Dutch Shell and ExxonMobil Corp, said on Sunday production was unaffected so far, but they were preparing for possible evacuations of workers and temporary output shutdowns.
Traders were also nervous supplies could be disrupted as a result of tension between the West and the world's fourth largest oil producer Iran.
Iran and the representative of six world powers talked by telephone on Monday about Teheran's disputed nuclear programme, but the Islamic Republic said it would press ahead in spite of a demand to halt the work.
Teheran failed to meet Saturday's informal deadline to respond to a package of incentives offered by the six powers.
Oil supplies have already been disrupted from Nigeria, the world's eighth largest oil exporter, as a result of militant attacks that have cut about a fifth of its production.
Gunmen kidnapped two French expatriates near the country's oil industry hub of Port Harcourt in the restive Niger delta, military and security sources said on Sunday.
Roads and Transport Authority has been working round the clock to carry out maintenance work
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