British oil giant BP on Monday said the cost of cleaning up the oil spill in the Gulf of Mexico has reached 2.65 billion U.S. dollars.

The bill includes the cost of the spill response, containment, relief well drilling, grants to the four Gulf states, claims paid, and federal costs, BP said in a statement.

Earlier this month, BP agreed to create a 20-billion-dollar escrow fund to pay for damage claims related to the worst oil spill in U.S. history.

BP said that to date, more than 80,000 claims have been submitted and almost 41,000 payments have been made, totaling more than 128 million dollars.

Meanwhile, the company said the construction of two relief wells, which are considered the best hope of stopping the oil leaking from the ruptured underwater well, are on track.

The first of the two relief wells has reached a depth of 16,546 feet (5,043 meters) and the leaking well was detected in a test called "ranging" run, BP said. A second similar test was also done.

"Drilling and ranging operations will continue over the next few weeks as the well progresses towards the target intercept depth of approximately 18,000 feet (5,486 meters)," BP said.

"Once intercept has occurred, operations are expected to begin to kill the flow of oil and gas from the reservoir by pumping specialized heavy fluids down the relief well," it said.

As relief wells saw progress, BP said Monday its plan to nearly double the amount of oil it can collect from the leaking well will be delayed for about a week by high waves expected from tropical storm Alex.

U.S. government scientists estimate 30,000 to 65,000 barrels of oil are gushing into the Gulf of Mexico a day.

Two oil containment systems in the Gulf of Mexico captured a total of about 22,750 barrels of oil Saturday, according to a BP statement.

BP said it's installing the first floating riser for a third oil-collecting vessel, which is expected to be ready at the end of this month or in early July.

This system is intended to increase oil containment capacity by 20,000-25,000 barrels a day.

But Kent Wells, BP's senior vice president of exploration and production, said Monday that waves of up to 12 feet (3.7 meters) from Alex could force a week-long delay in building the third oil-collecting system.

Alex will likely strengthen into the first hurricane of the 2010 Atlantic season on Tuesday before reaching the Texas-Mexico border early on Thursday, according to the U.S. National Hurricane Center.

The storm may affect efforts to clear the massive oil spill on the U.S. side of the Gulf of Mexico.

However, Wells said, BP's plan to boost oil containment capacity to 80,000 barrels per day by mid-July remains on track and that the company's oil-collecting operations will not be interrupted "unless unfortunately a storm heads directly our way."