By Arathy Somasekhar and Andrew Hayley

(Reuters) -Oil prices on Tuesday built on gains made a day earlier amid attacks on shipping in the Red Sea that have exacerbated supply worries.

futures rose 36 cents, or 0.44%, to $82.89 a barrel by 0745 GMT, while U.S. West Texas Intermediate crude futures (WTI) were up 31 cents, or 0.40%, to $77.89 a barrel.

"Concerns around shipping disruptions in the Red Sea have supported a rebound in the price of crude oil overnight, offsetting a more hawkish Fed currently weighing on the demand side of the equation," said Tony Sycamore, an analyst at IG in Sydney.

The attacks by Iran-aligned Houthis in support of Palestinians have increased freight rates and shipping times. On Monday, U.S. Central Command said that the Houthis had unsuccessfully fired a missile at the U.S. flagged oil tanker Torm Thor in the Gulf of Aden on Feb. 24.

On Tuesday, U.S. President Biden said Israel has agreed to halt military activities in Gaza for the Muslim holy month of Ramadan, as Hamas studied a draft proposal for a truce which includes a pause in fighting and a prisoner-hostage exchange.

Oil prices were also supported on Tuesday by indications of improved demand in China.

"Concerns over Chinese demand are abating, as refineries continue brisk buying in the physical market after a boom in Lunar New Year travel. This is despite them having planned more maintenance halts than usual," analysts from ANZ Bank said in a note.

Also on Tuesday, Russian authorities announced a six-month ban on gasoline exports from March 1 to compensate for rising demand from consumers and farmers and to allow for planned maintenance of refineries.

Both oil benchmarks settled more than 1% higher on Monday which followed declines of 2%-3% over the previous week as markets factored in a greater likelihood that rate cuts might take longer to come.

Kansas City Federal Reserve Bank President Jeffrey Schmid on Monday used a debut speech on policy to signal that he, like most of his central banking colleagues, is in no rush to cut interest rates. High borrowing costs typically reduce economic growth and oil demand.

A market focus for the day will be the American Petroleum Institute industry group's weekly data on inventories which is due to be released at 4:30 p.m. EST (2130 GMT).

Analysts polled by Reuters on Monday estimated on average that crude inventories rose by about 1.8 million barrels in the week to Feb. 23.