Louisiana Gov. Bobby Jindal expressed support for the decision.
"We're at a point where we can't afford to make this worse," Jindal said. "We cannot afford for them to do damage to this well."
Concerns about the plan have centered on the piping inside the blown-out well that extends about 13,000 feet into the sea floor. If there are any weak spots in that pipe, high pressures could cause new leaks.
"They have to be very careful when they close it down," said Dr. Don Van Nieuwenhuise, a professor of geoscience at the University of Houston. "[They have to] make sure that pressure doesn't come up quickly and cause any of the pipes to rupture."
ABC News' Russell Goldman, Ned Potter and Zunaira Zaki contributed to this report.