Brent crude futures for June, which expire on Tuesday, were down by 51 cents, or 0.6%, to USD 88.99 a barrel by 0950 GMT. The more active July contract fell 27 cents, or 0.3%, to USD 87.94 a barrel.
U.S. West Texas Intermediate (WTI) futures were down 22 cents, or 0.3%, at USD 83.63 a barrel.
A Hamas delegation will visit Cairo on Monday for talks aimed at securing a ceasefire, a Hamas official told Reuters on Sunday.
"With little other fresh news, the possible cooling of the Gaza environment sees oil prices slip," said John Evans of oil broker PVM.
Meanwhile, Israeli airstrikes on the southern Gaza city of Rafah on Monday killed at least 20 Palestinians and wounded many others.
Markets were also on watch for the U.S. Federal Reserve's May 1 monetary policy review.
"The language and forward forecasts will be pored over by all market participants with magnifying glasses," PVM's Evans said.
Ahead of that, on Friday U.S. inflation data put a damper on rate cuts in the near future, rising 2.7% in the 12 months through March, above the Fed's target of 2%. Lower inflation would have increased the likelihood of interest rate cuts, which tend to stimulate economic growth and oil demand.
"The sticky U.S. inflation sparks concerns for 'higher-for-longer' interest rates", leading to a stronger U.S. dollar and putting pressure on commodity prices, independent market analyst Tina Teng said.
A stronger dollar makes oil more expensive for those holding other currencies.
Further weighing on the outlook for oil demand, China's industrial profit growth slowed down in March, official data showed on Saturday, in the latest sign of frail domestic demand in the world's second largest economy.
But oil prices could swing higher again if U.S. inventory data and China's PMI index show improvements this week, Teng said.
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