BP has installed a larger, tighter-fitting containment cap on the ruptured Gulf of Mexico wellhead that has been gushing with oil since the Deepwater Horizon explosion on 20 April, raising hopes of limiting damage during the looming hurricane season.

Crude oil continues to spill into the sea, but the company will begin testing the new cap's internal pressure this morning by closing its valves. It hopes to stop the flow until more permanent measures can be taken.

"It is expected, though cannot be assured, that no oil will be released to the ocean for the duration of the test," BP said. "This will not, however, be an indication that flow from the wellbore has been permanently stopped."

Work on installing the cap using robots a mile below the surface of the sea was successfully completed last night as efforts intensified to capture all the oil that has spilled out since the explosion that killed 11 people on 20 April.

The tests on the internal pressure in the well will take between six and 48 hours to establish whether the flow has been stopped or leaks remain elsewhere. The developments may mark a turning point in efforts to stop the flow until more permanent measures, including the drilling of two relief wells, can be completed by the middle of next month.

BP said this was the first time a sealing system of this type had been deployed at such depths or under such conditions.

It replaces a previous cap, fitted last month, which managed to contain only about half the escaping oil. Estimates put this at between 35,000-60,000 barrels a day. The new cap, it is hoped, will be able to siphon the entire flow for collection on the surface.

Former US coastguard Admiral Thad Allen, who is overseeing the US government response, said measurements during the test would provide valuable information about the condition of the well below sea-level. "[This] will help determine whether or not it is possible to shut the well for a period of time, such as during a hurricane or bad weather, between now and when the relief wells are complete," he added.

Allen said the tests could continue for more than two days if necessary, but that the government would stop "if the risks of doing further damage to the surrounding formation are significant".

The news comes as BP says the cost of clearing up the environmental and economic disaster in the Gulf and on its damaged shoreline has reached $3.5bn (£2.33bn).

There is also a growing public row over Barack Obama's efforts to stop new drilling projects in the Gulf. His administration has outlined a more limited ban following the anger at the president's attempts to implement a six-month moratorium. A federal court in Louisiana had struck down earlier proposals saying they were too broad.

The new cap-and-seal stack is larger than the previous one and is bolted over the top of the wellhead rather than clamped loosely over it. Doug Suttles, BP's chief operating officer of exploration and production, suggested the cap might be used to keep the well closed for a longer stretch. "Depending on the results, we'll either continue to contain the flow while we wait on the relief well or potentially be able to close the flow in," he said.

For the duration of the tests, the two underwater oil-siphoning systems, one of them just brought online on Monday, will be turned off, BP said.

Suttles said that even if the cap could shut off the flow, BP must still finish the relief well at an even greater depth so it can pump heavy drilling fluid and then cement to permanently plug the leak. Yesterday the first of two relief wells, begun on 2 May, was about 190ft (58m) from intersecting the blown-out well 13,000ft beneath the seabed, Suttles said. The relief well could reach its target by the end of this month, BP said, keeping it on schedule to actually kill the leak by mid-August.

If the relief wells fail, BP could install a new permanent oil-capture system by late August or early September, Kent Wells, senior vice president of exploration and production, told Obama's commission investigating the spill.