October 7 (Reuters) - Oil prices steadied on Tuesday as sentiment, which had been boosted by a smaller-than-expected OPEC+ output increase, weakened due to weak global demand and the possibility of a supply glut.

Brent crude futures rose 1 cent, or 0.02 percent, to $65.48 a barrel by 0014 GMT. U.S. West Texas Intermediate (WTI) crude settled at $61.69 a barrel.

Both crudes rose by more than 1 percent at settlement in the previous session.

"Crude oil prices rose after OPEC announced a smaller-than-expected increase in production. The oil market had been anticipating a significant increase in quotas from the group's members who met to discuss the supply agreement" earlier this week, ANZ analyst Daniel Hynes wrote in a note to clients.

"This has allayed fears of a larger surplus than the market expected in the coming months," he added.

The OPEC+ group, which includes the Organization of the Petroleum Exporting Countries (OPEC), Russia, and some smaller producers, decided to increase its oil production by 137,000 barrels per day, starting in November.

The group raised its targeted oil production by more than 2.7 million barrels per day this year, equivalent to about 2.5 percent of global demand.

Geopolitical factors supported prices, as the conflict between Russia and Ukraine impacted energy assets and raised uncertainty about Russian crude supplies.

Two industry sources said on Monday that the Russian oil refinery Kirishi shut down its most productive distillation unit after a drone attack that caused a fire on October 4, and that repairs are likely to take about a month.

However, analysts said oil prices have come under pressure as investors see the potential for a supply surplus with increased supplies from OPEC+ and non-OPEC producers. Furthermore, any slowdown in demand due to weak economic growth caused by US tariffs is likely to exacerbate the surplus.

(Prepared by Duaa Muhammad for the Arabic edition)