Brent crude futures for November were up 20 cents, or 0.3% at USD 74.69 a barrel at 0045 GMT. U.S. crude futures for November were up 22 cents, or 0.3%, at USD 71.22.
Both contracts rose in the previous session on support from the U.S. interest rate cut and a dip in U.S. supply in the aftermath of Hurricane Francine. Oil prices climbed last week for a second week.
Last Wednesday, the U.S. Federal Reserve cut interest rates by half a percentage point, a larger decrease in borrowing costs than many expected.
Interest rate cuts typically boost economic activity and energy demand, but analysts and market participants are concerned the central bank may see a slowing job market.
"Sentiment was buoyed by the Fed's rate cut amid hopes it can engineer a soft landing for the economy," said ANZ . "A weaker US dollar also supported investor appetite."
ANZ also said that the fighting between Israel and Iranian-backed militias has raised concerns that the conflict will drag in Iran, a major oil producer in the region.
Hezbollah, an Iranian-backed group based in Lebanon, and Israel exchanged heavy fire into Sunday, as the group sent rockets deep into northern Israeli territory after facing some of the most intense bombardment in almost a year of conflict.
The conflict has escalated sharply in the past week after thousands of pagers and walkie-talkies used by Hezbollah members exploded. The attack was widely blamed on Israel, which has not confirmed or denied responsibility.
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