(CNN) -- The Department of Homeland Security has significantly increased the number of air marshals on flights since a failed Christmas terror attack on a U.S. jetliner, a department official told CNN Sunday.
The official, who asked not to be identified, said the ranks of the marshals have been increased by cutting vacations and leave, and by pulling in air marshals from instructional and administrative posts.
Homeland Security Secretary Janet Napolitano said there is no indication so far that the attack was part of a broad international effort.
"Right now we have no indication that it is part of anything larger," Napolitano told CNN's "State of the Union" program on Sunday.
A lone suspect allegedly tried to ignite an explosive device on a Northwest Airlines flight from Amsterdam, The Netherlands, to Detroit, Michigan, on Christmas Day.
The device apparently failed to detonate and the suspect was subdued.
On "State of the Union," Napolitano said air marshals are assigned randomly to flights.
"They are assigned on a random basis," Napolitano said Sunday morning, "They are assigned randomly on different flights."
Current and former marshals contacted by CNN took exception to Napolitano's claims, saying that while there is an element of randomness to increase unpredictability, the assignments of air marshals are largely based on intelligence and an analysis of which flights are most vulnerable or most attractive to terrorists.
In the Christmas incident, the suspect, Umar Farouk Abdulmutallab, was on a broad security watch list that contains "half a million" names and is shared with airlines and foreign security agencies, Napolitano said.
However, a lack of specific evidence prevented him from being classified as a greater security risk that would bar him from travel to the United States, she said.
"You need information that is specific and credible if you're going to bar people from air travel," Napolitano said.
Despite a possible tragedy, Napolitano said the response system worked as passengers and crew avoided panic and subdued the suspect while authorities notified other flights in the air of the situation and kept the air transport system operating.
"The whole process of making sure that we respond properly, correctly and effectively went very smoothly," Napolitano said.
There was no air marshal on the Northwest flight of the same route and flight number Sunday, a source with knowledge of the situation said, the same day it experienced another security scare.
The plane's crew was alerted over a passenger who spent a prolonged time in the bathroom, and the plane was met by law enforcement officials on the tarmac. Officials said the incident was unrelated to terrorism and that the passenger was just sick.
While the incident was a false alarm, Rep. Peter King, R-New York, also said it was his understanding there were no air marshals on the Sunday flight -- but there should have been.
"This was a clear failure of judgment," King told CNN's Jeanne Meserve Sunday. "There was a terrible mistake. It makes you wonder what world the administration is living in. If there was any flight that should have had an air marshal on board, it was the Northwest flight coming out of Amsterdam to Detroit."
King was not critical of the fact that no marshal was on the Christmas flight. "The reality is that you can't have federal air marshals everywhere. These are judgment calls. It would really be Monday-morning quarterbacking to say they should have had one on Christmas Day, but clearly they should have had one today."
Security screening has been increased in the wake of the incident, with different procedures at different airports to prevent predictability, Napolitano said.
"While we continue to investigate the source of this incident, the traveling public should be very confident of what we're doing now," she said.