(CNN) -- Robot submarines steered a new cap to BP's ruptured undersea well in the Gulf of Mexico on Thursday in the company's latest attempt to rein in the largest oil spill in U.S. history.

The cap was placed atop the pipe before 10 p.m., but oil and gas continued to spew as engineers attempted to adjust it.

BP CEO Tony Hayward announced that the company had crossed a "milestone" earlier in the day by cutting away the remains of the well's damaged riser pipe. That cleared the way for the dome to be lowered down to the well, 5,000 feet below the surface of the Gulf, but Hayward said the operation would need several more hours to complete.

"The next 12 to 24 hours will give us an indication of how successful this attempt will be," Hayward told reporters at the company's U.S. headquarters in Houston, Texas.

A Coast Guard spokesman predicted the operation would be completed sometime Thursday night, but said it would not be immediately known whether the cap was working.

Thursday's developments followed days of setbacks for workers trying to cap the well, which has spewed hundreds of thousands of barrels of oil a day into the Gulf of Mexico for six weeks.

An effort to slice off the pipe with a precision diamond-edged cutter failed Wednesday, forcing BP to settle for a rougher cut of the pipe made with shears. The more primitive cut means that a rubber seal will not be as tight as previously hoped, meaning a dome won't completely contain the spill, said U.S. Coast Guard Adm. Thad Allen, the federal government's response manager.

Nevertheless, Allen called Thursday's news "extremely important."

"I know they're working hard at it right now," he told CNN in an interview aboard one of the drilling platforms working on the relief well. "Even as we're talking here, it's happening 5,000 feet below us."

But the well may not be completely sealed off until at least until August, when BP hopes to complete a relief well. Hayward, whose company is responsible for containing the spill, said BP will be working to clean up the mess left behind "for a very, very long time."

"Our task is to contain the oil, ultimately to eliminate the leaking well and, most importantly, to clean up the oil, defend the shoreline and restore the shoreline where the oil comes ashore, so we return it to the original state," he said.

CNN Live: Underwater video from BP

Hayward's remarks come on day 45 of the disaster, as oil drifted eastward toward Florida and President Obama announced he will return to Louisiana on Friday to assess the latest efforts to counter the spill.

Obama told CNN's Larry King on Thursday that "BP caused this spill ... [and] they're responsible" for paying cleanup costs. "My job is to make sure they're being held accountable," he said.

The company has the "best equipment" to stop the spill, but he hasn't seen enough of a rapid response from BP, he said in an interview with to be broadcast Thursday night.

The president said he is "furious at this entire situation" in the Gulf because "somebody didn't think through the consequences of their actions."

Obama says his job is to fix things

Meanwhile, BP, under fire from seemingly every angle, launched a national ad campaign to improve its tarnished reputation. The beleaguered oil giant released television spots featuring Hayward, who apologizes and promises to "make this right."

Hayward stars in apology ad campaign

Even as the ads began to air, a grass-roots campaign dubbed Seize BP planned to kick off a week of demonstrations in more than 50 cities.

"From Florida to Seattle, Washington, from Hawaii to New York, all over California and many, many states across the country, people will be taking to the streets over the next week to demand that the assets of BP be seized now," said Richard Becker, a member of the San Francisco chapter of the group.

"We know millions of people are deeply concerned about what's going on in the Gulf right now, and we expect large numbers of people to come out to the protests."

Anti-BP sentiment has grown as oil has made its way to or near coastal areas. And the company has come under increasing fire from state governments and the Obama administration, which announced a criminal investigation into the spill and cut off joint news conferences with the company this week.

Oil has hit barrier islands off Mississippi and Alabama, and was only six miles off the Florida Panhandle on Thursday morning, state emergency management officials have reported.

After touring the area by helicopter, Florida Gov. Charlie Crist said he had seen "some light sheen" three to four miles from shore.

In Louisiana, where oily sludge has been fouling coastal marshes for two weeks, state officials said the White House has given its blessing to a plan to dredge up walls of sand offshore, and BP agreed to fund the $360 million construction cost.

But Gov. Bobby Jindal said Thursday that state officials "haven't gotten a dime from them."

"I'm calling on BP to step up [and] be the responsible party in fact, not just by label," Jindal said. He added, "We're done talking to attorneys."

BP announced Thursday on its website that it has established a $360 million escrow account to fund construction of the six sections of Louisiana barrier islands approved by federal authorities. "Since the environmental implications of the projects are not fully understood, BP assumes no liability for unexpected or unintended consequences of these projects," the company said in a posting on its website.

The BP well erupted after an explosion and fire on the leased Deepwater Horizon drilling rig on April 20 that killed 11 people. The rig sank two days later, leaving up to 19,000 barrels (798,000 gallons) of oil pouring into the Gulf, according to federal estimates.

CNN's Kyra Phillips, David Mattingly, Tracy Sabo, Patrick Oppmann, Scott Bronstein, Patty Lane and Aaron Cooper contributed to this report.