(CNN) -- Oil company BP says it has resumed pumping oil to a ship on the surface after a weekend setback that halted efforts to siphon off the crude spewing from a damaged well at the bottom of the Gulf of Mexico.

Crews re-inserted the tube into the well's riser stack Sunday. The 4-inch pipe is now connected to a ship on the surface, 5,000 feet above the sea floor, and is pumping oil back to the surface, BP spokesman Mark Proegler told CNN.

If successful, the technique will capture most of the oil that is pouring out of the well. The well has been spewing an estimated 210,000 gallons, or 5,000 barrels, of light sweet crude a day into the Gulf since the sinking of the drill platform Deepwater Horizon in late April.

"In terms of containing the flow, this was a positive step forward," said Kent Wells, a senior vice president for BP.

Wells said that crews were operating the tool cautiously as they make adjustments to achieve an optimal flow rate up to the drill ship.

"We'll look over the next day or two as we continue to optimize this to see the impact we can have on reducing the amount of flow" from the ruptured pipe, he said.

Homeland Security Secretary Janet Napolitano and Interior Secretary Ken Salazar issued a joint statement Sunday expressing caution about the effectiveness of the insertion tube.

"This technique is not a solution to the problem, and it is not yet clear how successful it may be," the statement said. "We are closely monitoring BP's test with the hope that it will contain some of the oil, but at the same time, federal scientists are continuing to provide oversight and expertise to BP as they move forward with other strategies to contain the spill and stop the flow of oil."

The effort was dealt a setback Friday night, when the frame holding the insertion tube shifted and prevented the surface vessel from connecting to it, said Doug Suttles, BP's chief operating officer for exploration and production.

The system was able to capture some of the leaking oil and pipe it aboard a drill ship on the surface overnight and burned off some of the natural gas released in the process, according to a statement from the joint BP-Coast Guard command center leading the response to the oil spill.

Wells said the next step in stopping the flow will be a "top kill" procedure in which a large amount of kill mud -- a heavy fluid used in drilling operations -- is inserted into the well bore to reduce pressure and reduce flow.

Once the pressure is reduced, BP hopes to be able to entomb the well in cement, effectively cutting off the gusher.

The statement from Napolitano and Salazar emphasized the importance of that step, saying "We will not rest until BP permanently seals the wellhead, the spill is cleaned up, and the communities and natural resources of the Gulf Coast are restored and made whole."

Wells said the mud will be pumped through the bottom of the well's blowout preventer at a maximum rate of 40 barrels (1,680 gallons) a minute.

"So with all of the pumping horsepower we have on the surface, we'll be able to pump far faster than the well can flow, and it's about us outracing the well," he said.

Preparations for the top kill procedure will take place over the next seven to 10 days, Wells said.

The slick from the spill has spread across much of the northern Gulf of Mexico, with bits of oil washing up periodically onto the shores of Louisiana's barrier islands.

Suttles said the application of underwater dispersants -- a tactic approved for use Friday -- appears to be working.

"The oil in the immediate vicinity of the well and the ships and rigs working in the area is diminished from previous observations," he said after flying over the area Saturday.

The Coast Guard and the Environmental Protection Agency said Friday that the decision to use subsea dispersants is an "important step" aimed at reducing potential damage from the spill, because dispersants can be more effective underwater than on the ocean's surface.

But more recent estimates suggest the actual volume of oil could be far higher than the estimated 5,000 barrels per day.

Ray Highsmith, executive director of the University of Mississippi's National Institute for Undersea Science and Technology, said that plumes of oil appear to have settled beneath the surface.

"We're clearly detecting something," Highsmith said. Either oil has settled on the bottom or it has risen to the surface and sunk again, as happened in the 1989 Exxon Valdez oil spill.

"This is a very different spill than we've ever had before, and we need to learn as much about it as we can," he said.

The underwater gusher began after an April 20 explosion aboard the drilling rig Deepwater Horizon. The explosion and subsequent fire caused the Deepwater Horizon to sink two days later, prompting oil to begin spilling from the well. BP was leasing the rig from Transocean.

CNN's David Mattingly and Eric Marrapodi contributed to this report.