February futures were little changed in New York after falling 1.2% on Friday, the most since Nov 29.
The shared neutral zone, which has been shut for at least four years due to disputes between the two countries, can produce as much as 500,000 barrels a day.
US explorers last week boosted drilling by the most in almost two years, according to data from Baker Hughes Co on Friday.
Oil is up more than 9% this month after the US and China struck a preliminary trade pact and the Organization of Petroleum Exporting Countries and its allies agreed to deepen output cuts.
Hedge funds increased bullish bets in the week ended Dec 17 to the highest level in more than seven months on rising crude prices, according to data released Friday.
“Oil prices will continue to benefit from positive developments in the US-China trade,” Stephen Innes, a market strategist at AxiTrader, said in a note.
“The seasonal demand slowdown in the first quarter could be an issue for this bullish view.”
West Texas Intermediate for February delivery fell 16 cents, or 0.3%, to US$60.28 a barrel on the New York Mercantile Exchange as of 11.47am Singapore time.
The contract declined 74 cents to settle at US$60.44 on Friday.
Brent for February settlement fell 17 cents, or 0.3%, to US$65.97 a barrel on the ICE Futures Europe Exchange.
The contract fell 40 cents to close at US$66.14 on Friday. The global benchmark crude traded at a US$6.70 premium to WTI.
Resuming output at the Wafra and Khafji oilfields in the neutral zone depends on a political decision and a final agreement, Kuwait’s Oil Minister Khaled Al-Fadhel said on Sunday.
Even if production resumes, the area wouldn’t add oil to global markets because both nations adhere to Opec supply limits, a person familiar with Saudi thinking said in October.
Working oil rigs in the US increased by 18 last week to 685.
In the Permian Basin of Texas and New Mexico, drillers deployed 15 additional rigs, wiping out several weeks of declines.