The cap has so far proved successful in stemming the flow of oil following the devastating Deepwater Horizon rig explosion in April.
The tests will find out if the steel casing of a cap placed over the well is strong enough to shut it off in the long term until relief wells are in place. BP started the tests on Thursday night.
They were due to finish on Saturday but the company decided to extend the examinations for a further 24-hour period.
A BP spokesman explained: "The cap is continuing to hold and the final tests will conclude tonight. Experts will be checking seismic results to determine pressure in the area.
"It's not a situation in which we will be able to say straight away if the cap has been successful. The results will need to be assessed."
Directors at the oil group are understood to have held discussions with its major shareholders over restructuring the company following the crisis, according to a Sunday newspaper.
Options under consideration are thought to include splitting up the group by selling its refineries and petrol stations, scaling back operations in the United States and doing more engineering in-house rather than outsourcing it.
The restructuring will come on top of the sale of around 10 per cent of the group's assets, which will be needed to meet the cost of the oil spill, which has so far reached $3.5bn (2.29bn).
Discussions with shareholders are said to be at an early stage, but they will be used to help to decide the direction of a formal strategic review, which is expected to be launched by the group's chairman, Carl-Henric Svanberg, once the ruptured well is finally sealed.
News that the leak was stopped on Thursday helped BP shares go higher at one stage on Friday, although wider stock market falls later pared back the gains.
It is thought the restructuring of BP could leave it a significantly smaller firm, which would focus on exploration in emerging oil regions, such as West Africa and Brazil, and lead to it selling its less profitable downstream arm.
The downstream business, which is made up of petrol stations and refineries, employs around 51,600 people – more than half of BP's 80,300 workforce – but accounts for only three per cent of the company's pre-tax profit.
Discussions are thought to be continuing between BP and US oil firm Apache Corporation over the sale of $12bn (7.84bn) worth of assets, including its stake in Alaska's Prudhoe Bay.
BP's board is understood to be due to meet later this week to discuss what assets will be sold off to pay for the oil spill.
As well as Prudhoe Bay, the group is also thought to be considering offloading its assets in Argentina, where it has a 60 per cent stake in oil company Pan American Energy worth around 3.5bn, as well as oil and gas fields in Vietnam, Colombia and Venezuela, worth around 1bn.
A BP spokesman declined to comment on the speculation.
BP said last month that it was making a 13bn fund available to compensate people who had been affected by the Gulf of Mexico oil spill.