A standoff between BP and the US government over the handling of the stricken Macondo well in the Gulf of Mexico continued with a sharp exchange of words over the best way to keep the oil contained before the well is permanently plugged next month.

Thad Allen, the official appointed by Barack Obama to lead the federal response to the disaster, gave BP another 24 hours in which to keep the new containment cap on the broken well closed.

But he warned that the US government would reserve the right to reopen the well if worries about seepage intensify.

Allen sent a stiff letter to BP on Sunday night, ordering the oil giant to continue seismic and sonar monitoring around the well to try to get a better picture of what was happening now that the flow of oil had ostensibly stopped.

He said the company had an obligation to inform him of any problems within four hours of any seepage being detected.

"I remain concerned that all potential options to eliminate the discharge of oil be pursued with utmost speed until I can be assured that no additional oil will spill from the Macondo well," he wrote.

At the heart of the dispute is anxiety about what is happening under the seabed. The government fears oil may be leaking below the surface, and that if left unchecked this process could cause graver problems, including the collapse of the well.

In a statement on Monday, Allen said he would ensure BP continues to assess whether keeping the cap closed could "worsen the overall situation".

BP, on the other hand, has pointed out forcefully that the antidote to seepage – reopening the cap and allowing the oil to flow again up to specially designed oil-capture vessels – would involve allowing oil to spew once more into the waters of the Gulf for at least another three days.

That would undo the sense of progress achieved since last Thursday, when the cap was fully locked down and the oil flow ceased.

Allen last night gave further details about the administration's worries. A seepage had been found three miles from the well, he said, but the indications were that this had nothing to do with Macondo. Bubbles had also been seen around the new cap, though he said that these did not seem to be in serious quantities.

The main way of tracking what is happening to the well – its "integrity", as it is known in the business – is to gauge the pressure of the oil that is flowing up the pipe. BP said on Monday that the level was about 6,800lbs per square inch (psi) and increasing at around 2 psi per hour.

The oil firm sees that as a positive figure, given that the quantity of oil in the reserve beneath the sea floor has already been depleted substantially, more than 4m barrels having spewed into the Gulf. But the Obama administration thinks this is lower than it should be and would like to see the pressure rise to around 8,000 psi, which would show conclusively that no leaks were taking place. Until that figure is reached, it will remain cautious, mindful of the political damage that has been caused to Obama's presidency as a result of his early handling of the crisis, which was criticised for being soft on BP.

Both sides are agreed that the disaster will not be fully over until permanent capping of the well is achieved through the drilling of relief wells. BP said the first relief well has reached 5,450 metres, and the second 4,840 metres. The relief wells could join up with the Macondo as early as next week, at which point heavy mud and then concrete will be pumped down the original well to block it forever.