NEW ORLEANS, LA --BP hopes to keep using its giant cork to block oil from reaching the Gulf of Mexico until they plug the blown out well permanently. "No one associated with this whole activity ... wants to see any more oil flow into the Gulf of Mexico," said Doug Suttles, BP's chief operating officer. "Right now we don't have a target to return the well to flow." Pressure in the well cap continues to rise, and scientists are still monitoring for any signs of a leak, but the news still seems to be good, Suttles said. The oil giant is hoping to keep evaluating even after the extended monitoring period it was given by the government, which expires Sunday afternoon. "We're not seeing any problems at this point with the shut-in," Suttles said at a Sunday morning briefing. Retired U.S. Coast Guard Adm. Thad Allen, the government's point man on the crisis, gave the oil giant at least three days to see whether its stopgap measure would work. He said Saturday that after the test was complete, the cap is to be hooked up through nearly a mile of pipes stretching to ships on the surface that will collect the oil. But that would mean oil would flow back into the Gulf for three days, Suttles said, something no one wants to see. Suttles said the oil giant hopes to keep the well shut in until it's permanent measure is completed. BP is drilling two relief wells, one of them as a backup. Wells said work on the first one was far enough along that officials expect to reach the broken well's casing, or pipes, deep underground by late this month. Then the job of jamming it with mud and cement could take "a number of days through a few weeks." The cap stopped the crude Thursday for the first time since the April 20 explosion unleashed the spill.