Brent crude futures climbed 82 cents, or 1.1%, to $74.05 a barrel as of 0840 GMT. U.S. West Texas Intermediate crude was up 77 cents, or 1.1%, at $72.54.

Iran is the third-largest producer among members of the Organization of the Petroleum Exporting Countries and there is widespread concern the fighting could affect exports from there. Additionally, investors are watching for signs shipments through the Straits of Hormuz, through which flows about 19 million barrels per day of oil and oil products, may be impacted.

"The market is largely worried about disruption through Hormuz but the risk of that is very low, said Saxo Bank analyst Ole Hansen.

There have been no signs of supply losses but ships moving in the vicinity of the Strait and the Persian Gulf have been affected by electronic warfare measures that have interfered with navigation systems.

Early on Tuesday, shipping sources said a vessel collided with two other ships sailing near the Strait of Hormuz, highlighting the risks to companies moving oil and fuel supplies in the region.

Despite the potential for disruptions, there are signs oil supplies remain ample amid expectations for lower demand.

In its monthly oil report released on Tuesday, the International Energy Agency revised lower its world oil demand estimate by 20,000 bpd from last month's forecast, while increasing the supply estimate by 200,000 bpd from last month's estimate to 1.8 million bpd.

Investors are also focusing on central banks' interest rate decisions, Tamas Varga, analyst at PVM Associates said in a note, with the U.S. Federal Open Market Committee, which guides the Federal Reserves rate movements, set to meet later on Tuesday.