NEW ORLEANS — Officials worked Sunday to try to stop oil leaks coming from the deepwater well drilled by a rig that sank last week near Louisiana, but they acknowledged that it could be months before they are able to stem the flow of what is now about 42,000 gallons of oil a day pouring into the Gulf of Mexico.

The response team is trying three tacks: one that could stop the leaks within two days, one that would take months and one that would not stop the leaks but would capture the oil and deliver it to the surface while permanent measures are pursued.

Officials determined through weather patterns that the sheen of oil and water, now covering 600 square miles, would remain at least 30 miles from shore for the next three days. But states along the Gulf Coast have been warned to be on alert.

“We have been in contact with all the coastal states,” Rear Adm. Mary E. Landry, the commander of the Eighth Coast Guard District, said at a news conference on Sunday. Emphasizing that the sheen was not estimated to hit shore anytime soon, Admiral Landry said contingency plans were being put in place.