BP PLC, facing rising public anger in the U.S., began Monday its third attempt to contain oil from its leaking well in the Gulf of Mexico, but the risky operation could make the spill worse in the short term.

The latest procedure involves slicing off the leaking pipe at the top of the well's broken blow-out preventer, placing a cap over the leak and channeling the captured oil and gas to a vessel on the surface. BP officials said the procedure could take from four days to a week, and it already has two different caps on the...