The company said it does not expect the container to be fully operational until at least Sunday or Monday.
"It appears to be going exactly as we hoped," Bill Salvin, a BP spokesman, told The Associated Press news agency on Friday afternoon, shortly after the four-storey device hit the seafloor.
"Still lots of challenges ahead, but this is very good progress.
"We are essentially taking a four-storey building and lowering it 1,500 metres and setting it on the head of a pin."
While similar devices have been used in the past, they have never been tested at such a depth, and it was not clear whether it would function properly.
The device is designed as a stop-gap measure to cap the leak in one of three places while crews continue to drill a relief well to ease the pressure off the blown-out well at the site, but that could take up to three months to complete.
The rest of the oil is coming from the blowout preventer at the well, a heavy piece of machinery designed to prevent such a leak.
Wreckage of rig
The lowering of the containment box - which will be able to capture up to 85 per cent of the leaking oil - played out slowly 80km off the coast of Louisiana.
About 400 metres away is the wreckage of the drilling rig Deepwater Horizon, which BP was leasing when it exploded on April 20, blowing open the well and triggering a major environmental crisis.
Eleven workers were killed in the accident at the platform, which sank two days later.
An estimated 800,000 litres of oil have been spewing daily ever since, in the biggest oil spill in the US since the Exxon Valdez disaster in Alaska in 1989.
So far about 11 million litres of crude have spilled to sea, sending oil slicks toward a shoreline of marshes, shipping channels, fishing grounds and beaches in four US states.
The operation to contain the spill came as oil sheen was seen spilling on islands off the coast of the southern US state of Louisiana, the US coast guard said.
The move to cap the leak took on an added urgency as oil reached several barrier islands off the Louisiana coast, many of them fragile animal habitats.
"Teams have confirmed oil on Freemason Island," Petty Officer Connie Terrell of the US coast guard said on Thursday.
"It is at the south end of the Chandeleur Islands. It is largely sheen with no evidence of medium or heavy oil."
Oil sheen is the shimmering thin layer of crude settled on top of water.
Several birds were spotted diving into the oily, pinkish-brown water, and dead jellyfish washed up on the uninhabited islands.
Huge oil slick
Meanwhile, a huge oil slick is floating in the Gulf, and residents of Louisiana, Mississippi, Alabama and Florida are anxiously waiting for landfall.
Seas were calm on Friday, and the US Coast Guard hoped to continue skimming oil from the ocean surface, burning it at sea and dropping dispersants from the air to break it up.
John Curry, BP's spokesman, said that three emergency response teams were sent to the island, some 50km offshore, and were deploying inflatable booms to try to protect the prime marsh and wildlife area.
"This is the first confirmation of shoreline impact we have had," he said.
"We are doing everything we can to make sure a major impact doesn't happen."
The Chandeleur Islands form the easternmost point of Louisiana and are part of the Breton National Wildlife Refuge - the second oldest refuge in the US and home to countless endangered shorebirds.
Al Jazeera's Cath Turner, reporting from the Gulf of Mexico, said that water off the Mississippi coastline was now pinkish-reddish in colour, having been stained by oil and dispersant.
"The mostly fine weather has helped authorities contain the spill, but there's no telling how long that will last," Turner said.
She said that she had seen casualties of the oil- a bird that had been drifting in the slick for some time and was so weak that it could barely move.
"Its feathers were slippery with oil sheen ... it didn't have long to live."