HOUSTON — The fighting is not yet over in Tripoli, but the scramble to secure access to Libya’s oil wealth has already begun.

Before the rebellion broke out in February, Libya exported 1.3 million barrels of oil a day. While that is less than 2 percent of world supplies, only a few other countries can supply equivalent grades of the sweet crude oil that many refineries around the world depend on. The resumption of Libyan production would help drive down oil prices in Europe, and indirectly, gasoline prices on the East Coast of the United States.

Western nations — especially the NATO countries that provided crucial air support to the rebels — want to make sure their companies are in prime position to pump the Libyan crude.

Foreign Minister Franco Frattini of Italy said on state television on Monday that the Italian oil company Eni “will have a No. 1 role in the future” in the North African country. Mr. Frattini even reported that Eni technicians were already on their way to eastern Libya to restart production. (Eni quickly denied that it had sent any personnel to the still-unsettled region, which is Italy’s largest source of imported oil.)