"This is generally good news," he said, but cautioned that "we need to be careful not to do any harm or create a situation that cannot be reversed".
Allen ordered further study and said the testing would go on into the night to determine whether BP's capped oil well was holding tight or in danger of springing a new leak.
Al Jazeera's John Terrett, reporting from New Orleans, said that BP could decide to reopen the cap and allow some oil to spill into the sea again if pressure drops. But the company said that this would be done in a controlled manner, unlike the unabated flow that has gone on for much of the past three months.
Wells spoke to the media two hours after Allen did and sounded more upbeat than the retired admiral.
"We won't be done until we actually know that we've killed the well ... I don't want us to get too far ahead of ourselves"
"I'm very excited to see no oil flowing into the Gulf of Mexico," Wells said.
But throughout the day, no one was declaring victory just yet.
Barack Obama, the US president - who has seen his approval ratings drop as the crisis has dragged on - called the apparent success of BP's efforts "good news" on Friday.
But he cautioned the public "not to get too far ahead of ourselves", warning of the danger of new leaks "that could be even more catastrophic".
"The new cap is good news, either we will be able to stop the flow or we will be able to capture all the oil until the relief well is done," he said.
"[But] we won't be done until we actually know that we've killed the well and that we have a permanent solution in place. We're moving in that direction, but I don't want us to get too far ahead of ourselves."
Plugging the leak
On Thursday, BP closed the vents on the new, 75-tonne tight-fitting metal cap and finally stopped crude from spewing into the Gulf of Mexico for the first time since the April 20 oil rig explosion that killed 11 workers and unleashed the spill about 1.6km below the surface.
Experts say between 35,000-60,000 barrels of oil have been pouring into the Gulf of Mexico daily for about 13 weeks, threatening vulnerable wildlife and fouling the shores of five US Gulf states.
|The oil spill has already caused massive environmental damage [Reuters]
With the cap working like a giant cork to keep the oil inside the well, scientists have been keeping watch in case the buildup of pressure underground causes new leaks in the well pipe and in the surrounding bedrock that could make the disaster even worse.
Pressure readings after 24 hours were about 6,700 pounds per square inch and rising slowly, Allen said on Friday, below the 7,500 psi that would clearly show the well was not leaking. He said pressure continued to rise between 2 and 10 psi per hour.
A low pressure reading, or a falling one, could mean the oil is escaping.
But Allen said a seismic probe of the surrounding sea floor found no sign of a leak in the ground.
The cap is designed to prevent oil from spilling into the Gulf, either by keeping it bottled up in the well, or by capturing it and piping it to ships on the surface.
It is not yet clear which way the cap will be used if it passes the pressure test.
Either way, the cap is a temporary measure until a relief well can be completed and mud and cement can be pumped into the broken well deep underground to seal it more securely than the cap.
The first of the two relief wells being drilled could be done by late July or August.
In a positive sign, work on the relief wells resumed on Friday after it had been suspended earlier in the week for fear that the capping of the well could interfere with it.
But even if the cap proves successful and the relief well drilling continues without a hitch, BP's troubles will not be over as it faces 307 court cases being brought by fishermen, tourist resorts and boat captains who claim their businesses have been completely wrecked this summer by the oil spill.
And on Friday, fishermen in Mississippi walked out of a town hall meeting in Biloxi in protest after Kenneth Feinberg, the federal official in charge of administering BP's $20bn compensation fund, said money the fishermen earned doing clean-up work for BP would be subtracted from their claim against the company.
"I am furious about this," said Tuget Nguyen, a fisherman. "If he takes away the money we are making from BP when we get our claims, then nobody is going to work for BP to clean up this oil and we will not rent our boats to BP either. It is not fair."
Thousands of fishermen in Louisiana, Mississippi, Alabama and Florida, out of work because federal authorities have closed much of the Gulf to fishing, are working for the Vessels of Opportunity programme, skimming oil from the water and protecting coastlines.
Meanwhile, the massive job of cleaning up the government estimated 356 million and 697 million litres of oil spilled into the Gulf continues.
Tim Kerner, the mayor of Lafitte, Louisiana, said the crisis was not over by a long shot.
"There's millions and millions of gallons of oil out there, and they need to keep the fishermen working," he said. "It's no time to pull back. It's time to continue to fight until we know it's over.
"I don't want everybody to think we won this battle. This battle's going to be ongoing for a while."