The US president said he would meet company executives later and tell them that they must set up a fund to compensate those affected by the spill.
He described the spill as an assault on the shores and citizens of the US that tested the limits of human technology.
Presidents use the Oval Office for what they regard as vital national issues.
The speech comes as opinion polls suggest a majority of Americans disapprove of how Mr Obama has handled the crisis - the worst environmental disaster in US history. 'Mutual goals'
In his speech, Mr Obama likened the spill to an "epidemic" and reiterated that BP would be made to pay for the damage.
Mr Obama said he would meet BP Chairman Carl-Henric Svanberg on Wednesday and "inform him that he is to set aside whatever resources are required to compensate the workers and business owners who have been harmed as a result of his company's recklessness".
In response to the speech, BP said in a statement that it shared Mr Obama's goal of cleaning up the oil and helping the people affected by the spill.
The firm said it was looking forward to Wednesday's meeting "for a constructive discussion about how best to achieve these mutual goals".
Mr Obama also used the speech to renew calls for the US to embark on a future of clean energy.
But he gave few details and made no pledges about specific legislation, instead promising to look at ideas from Republicans and Democrats on the issue.
He also announced that the national commission he set up to investigate the causes of the oil spill would be headed by Ray Mabus, a former governor of Mississippi.
With this speech, the president has made a lofty appeal to American idealism, analysts say, but that appeal will not be universally welcomed at a time when Americans are mostly worried about the more pressing need simply to stop the leak.
The Republicans were quick to criticise the address, with party chairman Michael Steele accusing Mr Obama of exploiting the crisis for his own political gain.
Oil has been spewing into the Gulf of Mexico since a drilling rig leased by BP exploded on 20 April.
BP managed to place a cap over the leaking oil pipe earlier this month, and is now siphoning off much of the oil.
But estimates of how much oil was gushing out of the well before the cap was put in place have risen dramatically.
Initially experts said about 15,000 barrels were leaking each day, but scientists now believe the figure to be between 35,000 and 60,000 barrels.
US Congressmen have been fiercely critical of BP, accusing its executives of failing to follow proper procedures.
Politicians have spoken of legal action - and even the possibility of criminal charges - against BP.
As the rhetoric has become increasingly bitter, the firm's share price has continued to tumble, with billions of dollars being wiped off its value.
BP's much-anticipated attempt to cap its undersea gusher in the Gulf of Mexico, a spill now estimated at twice the size of the Exxon Valdez disaster, was suspended for more than 16 hours before it was restarted late Thursday afternoon, a BP executive said Thursday.
"This whole operation is very, very dynamic," Doug Suttles, the company's chief operating officer.
"When we did the initial pumping (Wednesday), we clearly impacted the flow of the well. We then stopped to monitor the well. Based on that, we restarted again. We didn't think we were making enough progress after we restarted, so we stopped again."
The light-brown material that was seen spilling out of the well throughout Thursday was the previously pumped fluid from the "top kill" procedure mixed with oil, he said.
"I probably should apologize to folks that we haven't been giving more data on that," Suttles said when asked why it took so long for BP to announce it had suspended the top kill. "It was nothing more than we are so focused on the operation itself."
Suttles said part of the problem is that too much mud is leaving the breach instead of going down the well. "So what we need to do is adjust how we are doing the job so that we get more of the drilling mud to go down the well," Suttles said.
He said one solution would be to introduce solids -- known as "bridging material," or its variant "junk shot" -- into the mix.
BP officials say the procedure could take another 24 to 48 hours to complete, though whether the top kill will successfully stop the flow of oil is uncertain.
Enormous brown plumes of drilling "mud" billowed from the damaged well during the process, which BP Managing Director Bob Dudley called "a "titanic arm-wrestling match" a mile below the surface.
Coast Guard Adm. Thad Allen, who is leading the government's response to the oil spill, earlier said the work "is moving along as everyone had hoped."
"They're pumping mud into the well bore, and as long as mud is going down, hydrocarbons are not going up," Allen told reporters Thursday afternoon. The work could take another night, he told reporters in Venice, near the mouth of the Mississippi River.
"I think we just need to let that run its course, and we will see what happens," Allen said. However, asked about reports the procedure had been halted, Allen said he hadn't talked to BP officials yet.
Stopping the leak took on even more urgency after government scientists released spill estimates that far exceed the previous 5,000-barrel-a-day number given by BP.
The burst well is spewing oil at a rate of at least 12,000 to 19,000 barrels a day, U.S. Geological Survey Director Marcia McNutt told reporters Thursday, meaning 260,000 to 540,000 barrels had leaked as of 10 days ago -- larger by far than the 250,000 barrels spilled when the tanker Exxon Valdez ran aground in Alaska's Prince William Sound in 1989.
The 38-day-old spill was beginning to take its toll on Louisiana's sensitive coastal marshes, where heavy oil has been killing plant life and fouling local wildlife and fisheries. On Thursday, the eve of the Memorial Day holiday weekend, the beaches of Grand Isle were empty.
"If only it gets stopped, if what they did yesterday works, that's the beginning of the end," Grand Isle Tourism Commissioner Josie Cheramie said. "We can clean up what's already been put out there, but we just really need to get it stopped. That's the main thing."
The spill claimed a job in Washington, as the head of the scandal-plagued federal agency that oversees offshore drilling resigned.
BP is under intense pressure to succeed with its latest attempt to stem the leak, after previous measures failed.
Thousands of barrels of oil have been spewing into the Gulf every day since the accident on 20 April.
Mud will continue to be pumped into the well for hours, spokesman Steve Rinehart said.
"The procedure is intended to stem the flow of oil and gas and ultimately kill the well by injecting heavy drilling fluids through the blowout preventer on the seabed, down into the well," a BP statement said.
If the oil flow is successfully capped, engineers will follow up with cement to seal the well permanently.
BP Chief Executive Tony Hayward has put the operation's chance of success at 60-70%.
Officials say the method has been used before in other areas of the world, but not at the depths required to stem the oil from the Deepwater Horizon rig.
There is a risk a weak spot in the blowout preventer that sits on top of the well could breach under the pressure, causing a brand new leak at the site 50 miles (80km) off the Louisiana coast. 'No guarantees'
Speaking in California, US President Barack Obama said his administration would commit all resources necessary to stop the flow of oil into the sea.
Mr Obama said the "heartbreaking" oil spill underscored the need to find alternative energy sources.
"We will not rest until this well is shut, the environment is repaired and the clean-up is complete," he added.
Mr Obama is due to make his second visit to the Gulf of Mexico region on Friday.
His visit will come a day after he receives a report into offshore drilling that is expected to recommend tougher regulations and demand more safeguards.
London-based BP has acknowledged that a series of failures occurred on the Deepwater Horizon oil rig in the hours before the explosion that killed 11 workers and triggered the spill that has so far spewed at least 7 million gallons (26.5 million litres) into the Gulf.
In a memo, Representatives Henry Waxman and Bart Stupak say the explosion was preceded by several warning signs - including abnormal pressure readings and failures in some functions of the blowout preventer - but action appears to have been taken too late.
Questions have been raised over whether proper procedures were followed.
Speaking on US television on Wednesday, Mr Hayward said: "What we're seeing here is a whole series of failures. We've identified... at least seven.
"It's very clear that much more needs to be put in place to deal with this situation should it ever occur again."
He added: "It's clear that this will be a transforming event in the history of deep water exploration.
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