Producer nations in OPEC+, which includes Russia, will likely stick to a plan for accelerated oil output increases in August when they meet on Thursday, sources said.
But, for now, the pressing supply worries outweighed growing concerns over the potential for a global recession following a string of downbeat U.S. economic data.
Brent crude futures edged up 22 cents, or 0.2%, to $113.34 a barrel by 0342 GMT after rebounding 2.8% on Friday. U.S. West Texas Intermediate crude was at $107.73 a barrel, up 11 cents, or 0.1%, following a 3.2% gain in the previous session.
Both contracts posted their second weekly decline last week as interest rate hikes in key economies strengthened the dollar and fanned recession fear.
However, oil prices remained well supported above $100 a barrel while prompt monthly spreads remained wide in backwardation as crude and oil product supplies remained tight.
Backwardation occurs when prompt prices are higher than prices for delivery in future months, indicating tight supplies.
G7 leaders, who began their meeting on Sunday, are expected to discuss options for tackling rising energy prices and replacing Russian oil and gas imports, as well as further sanctions that do not exacerbate inflation.
These measures include a possible price cap on Russian oil exports to reduce Moscow's revenues while limiting damage to other economies.
"It's unclear whether a price cap will achieve this outcome," Commonwealth Bank of Australia analyst Vivek Dhar said in a note.
"There's still nothing stopping Russia from banning oil and refined product exports to G7 economies in response to a price cap, exacerbating shortage conditions in global oil and refined product markets."
G7 will also discuss the prospect of reviving the Iran nuclear talks after the European Union's foreign policy chief met senior officials in Tehran to try to unblock the stalled negotiations, a French presidency official said on Sunday.
In addition, some of the G7 leaders are pushing for an acknowledgement of the need for new financing for fossil energies investment, two sources told Reuters on Sunday, as European states scramble to diversify supplies.