US President Barack Obama has said there is much work to do despite no oil leaking from a cap sealing BP's Gulf of Mexico well for 24 hours.
"It is important we don't get ahead of ourselves," he said.
Incident commander Adm Thad Allen warned a test of the well did not show conclusively there were no other leaks.
He said the test would continue for several more hours at least before BP reassesses to see whether the well should be opened again.
Meanwhile, Mr Obama said: "One of the problems with having this camera down there is, is that when the oil stops gushing, everybody feels like we're done - and we're not."
A new cap was used on Thursday to stop the flow for the first time since 20 April, as part of a 48-hour test of the well's integrity.
Eleven workers were killed in the Deepwater Horizon explosion, and the oil spill has raised fears of an environmental catastrophe.
Spilled oil has affected hundreds of miles of Gulf coastline since April, with serious economic damage to the region.
BP has already paid out more than $200m (£130m) in claims to 32,000 claimants. A further 17,000 claims are being evaluated for payment, and more information is being sought on 61,000 other claims.
UK Prime Minister David Cameron also welcomed the progress after meeting BP chairman Carl-Henric Svanberg at 10 Downing Street.
"It seems as if they have had, touch wood, some success in the last couple of days," Mr Cameron said.
"They want to clean up the mess, they want to pay compensation to... everyone who has been affected, but they do need some sort of certainty that the compensation claims won't go into tertiary and sort of further claims which aren't really related to the mistakes that BP made."
On the sea floor there is currently no evidence of the well rupturing.
The flow of oil was shut off at 1425 local time (1925 GMT) on Thursday. The stoppage is part of a test of the integrity of the well.
If the pressure within the new cap on the well stays high, that could mean there are no other leaks or ruptures within the wellbore. If it drops, that could suggest problems.
The pressure within the well was at 6,700 pounds per square inch on Friday morning and steadily rising, said BP Vice-President Kent Wells.
If it were to drop below 6,000psi that would probably mean there was a problem within the well. If it continues rising and stays over 8,000psi that would probably mean the well was intact, Mr Wells said.
There is currently "no negative evidence of any breaching" of the sea floor, Mr Wells said. BP will soon run another seismic survey to check for any evidence of ruptures.
BP is also resuming work on a relief well that has 30ft left to drill before it hits the original leaking well. Once the wells intersect, mud and cement will be used to permanently deal with the leak.
The current pressure test could last for up to 48 hours, with BP and government experts reviewing results every six hours.
If the test is successful it is not clear what will happen next.
BP has suggested it might be possible to keep the well shut, with oil collection vessels left on standby.
Adm Allen has suggested the most likely outcome is the resumption of collection of the oil with four vessels and the capacity to collect 80,000 barrels - all or virtually all of the oil - each day.