British oil giant BP said Wednesday it hopes to start a technology known as "top kill" on Sunday or early next week to stop the massive oil spill in the Gulf of Mexico.

The so-called "top kill" is a two-step process where first, plugging agents are pumped into the blowout preventer to stop the flow. If successful, it will be followed by either heavy mud or cement that increases the hydrostatic head on the well, stopping the flow of the well.

The procedure, which could take several weeks to complete, would stop the oil that has been leaking from the ruptured undersea wellhead since the explosion and sinking of the Deepwater Horizon drilling rig off the Louisiana coast late April.

"This is all being done at a depth of 5,000 feet and it's never been done at these depths before," said Doug Suttles, operating officer for exploration and production of BP, which was leasing the Deepwater Horizon rig and now responsible for the clean-up in the Gulf.

In a news release issued Sunday, BP said it may combine "top kill" with so-called "junk shot", the injection under pressure of a variety of materials to seal off upward flow.

Since Sunday's insertion of a 4-inch tube into a 21-inch riser pipe that once connected the rig with the underwater well, BP said the tube has been capturing 2,000 barrels of oil a day from the leaking well. Tom Strickland, an assistant interior secretary, put the figure at 3,000 barrels a day.

As BP's oil-containment efforts progressed, Florida's tourism gained a respite when the U.S. Coast Guard said Wednesday laboratory tests had shown that 50 tar balls found this week on the Lower Keys -- a mecca for divers, snorkelers, fishermen and beach goers -- were not from the oil spill.

The spill has already sent oil ashore, especially in Louisiana but also on the coasts of Mississippi and Alabama, threatening fisheries and wildlife refuges along these coastal states.

However, local tourism authorities said, damage had already been inflicted by the negative publicity linked to the month-old spill.

"Even if we don't get even a gumball-sized tar ball down here in the next month, there has already been significant perception damage to Florida Keys and Florida tourism," Andy Newman, a local tourism official, was quoted by local media as saying. "We understand we are not out of the woods yet, that there's more oil out there."

U.S. and Cuban officials were reportedly holding "working level" talks on how to respond to the spill, adding to signs of concern that strong currents could carry the oil slick far from the site of the spill, possibly threatening the Florida Keys and the pristine white beaches along Cuba's northern coast.

Scientists were surveying the Gulf of Mexico to determine if the oil had entered a powerful current that could take it to Florida and Cuba.