A 20-year-old North Carolina man was being questioned by the FBI in connection with the incidents, according to a congressional official and a senior law enforcement official, both of whom spoke on condition of anonymity.
The congressional official said the man, described as a college student, had informed the Transportation Security Administration that he planned to put packages on planes in an effort to expose gaps in aviation security.
"It doesn't appear to be a terrorist event," FBI Director Robert Mueller said. "I think it is safe to fly."
Still, as a precaution, the government ordered intensified searches of the roughly 7,000 commercial aircraft. The checks were expected to be completed by Saturday, with no disruptions to service.
The suspicious bags were hidden in lavatory compartments aboard Southwest Airlines jets that landed in New Orleans and Houston. They were found late Thursday by maintenance workers.
A Southwest statement said the items appeared "intended to simulate a threat" and that each bag was accompanied by a note that "indicated the items were intended to challenge Transportation Security Administration checkpoint security procedures."
The items posed no actual safety threat but they raised new questions about the effectiveness of post 9-11 security. And that, sources say, was the motive behind the twin incidents, reports CBS News Correspondent Bob Orr.
Another senior law enforcement official, also speaking on condition of anonymity, said each note included precise information about where and when the items were placed on board the aircraft. The official would not provide further details.
In addition to the box cutters and notes, the bags contained bleach, matches and modeling clay, according to the official. The bleach on one of the planes was in a suntan lotion bottle and in another unidentified container on the other plane.
The clay was formed to look like a plastic explosive, while the bleach could have been used to demonstrate how a corrosive or dangerous liquid could be smuggled aboard an aircraft.
Though government officials were quick to say there were no indications of terrorism, the discovery aboard the Southwest planes was a chilling reminder of the Sept. 11, 2001, attacks. The 19 hijackers used box cutters to take over four jets that day. Box cutters and bleach are now are among the items that cannot be carried onto planes.
The TSA was created after the attacks, with the goal of replacing privately employed airport security workers with better-trained and higher-paid government employees. Problems with screening passengers and bags have persisted, however. For example, officials say X-ray machines can't detect plastic explosives.
Officials say it's unclear whether the items placed on the Southwest planes ever went through security. Investigators have interviewed passengers and crew on the New Orleans plane but also had not ruled out the possibility that airline or airport workers had placed the bags on the planes.
Southwest spokeswoman Beth Harbin said the New Orleans plane had originated in Orlando, Fla., and was scheduled to go on to San Diego later Thursday night. The crew reported a lavatory wasn't working and a maintenance worker discovered the bag while working on the problem at about 9 p.m., she said.
A short time later, a bag was found aboard the Houston aircraft, which had arrived from nearby Austin, Texas, for routine maintenance. Southwest said security checks of its entire fleet of 385 aircraft found no other suspicious items.
All airlines conduct routine searches of their planes. Homeland Security Department spokesman Brian Roehrkasse said a government directive that went out after the bags were found instructed airlines "to make sure the searches are done in a comprehensive and thorough manner."
Paul Rancantore, deputy chairman of the security committee for American Airlines' pilots union, described the routine searches as fairly perfunctory.
"It's kind of a walk-through. They're just looking for things that are obvious," Rancatore said. "There's no removing of panels, no dogs."
Rep. John Mica, chairman of the House aviation subcommittee, said the incident demonstrates the need to screen all employees with access to aircraft and whatever they bring on a board. He also said TSA needs improved technology to screen for explosives and banned objects.
"We need to have TSA get its act together and put in place the adequate training and technology to deal with the threat," said Mica, R-Fla.