Oil prices were little moved in early trading on Tuesday, as market participants assessed a visit to the Middle East by U.S. Secretary of State Antony Blinken to discuss a ceasefire offer in the region.

Blinken met Saudi Arabia's de-facto ruler on Monday. Palestinians hope the visit will clinch a truce before a threatened Israeli assault on Rafah, a border city where about half the Gaza Strip population is sheltering.

The ceasefire offer, delivered to Hamas last week by Qatari and Egyptian mediators, awaits a reply from militants who say they want more guarantees it will bring an end to the four-month-old war.

Brent crude futures were down 2 cents at $77.97 a barrel as of 00:01 GMT, while U.S. West Texas Intermediate crude futures edged down 3 cents to $72.75. Both contracts gained nearly 1% on Monday, rising for the first time in four sessions.

The United States continued its campaign against Iran-backed Houthis in Yemen, whose attacks on shipping vessels have disrupted global oil trading routes.

In Russia, two Ukrainian drones struck the largest oil refinery in the country's south on Saturday, a source in Kyiv told Reuters. It was the latest in a series of long-range attacks on Russian oil facilities, which has reduced Russia's exports of naphtha, a petrochemical feedstock.

Market participants awaited industry data due later on Tuesday on U.S. crude stockpiles. Five analysts polled by Reuters estimated on average that crude inventories rose by about 2.1 million barrels in the week to Feb. 2.

(Reporting by Stephanie Kelly; Editing by Edwina Gibbs)