In response to a reporter's question, Currier said, "I am not issuing an apology, because, although it's unfortunate that it escalated to this level, what you're seeing here is the result of a normal training exercise."
Coast Guard staff played a recording of the radio traffic during the drill. In it, a crew member on one boat is heard saying, "If you don't slow down, we're going to -- you will be fired upon. Roger, roger midzone."
Currier said the Coast Guard will reevaluate its communication procedures to prevent future misunderstandings.
A Coast Guard public affairs officer said that though weapons are mounted on the boats involved in the exercises, they are not loaded.
According to ABC News Senior White House Correspondent Jake Tapper, White House Press Secretary Robert Gibbs said he was not aware of any heads-up given by the Coast Guard to the White House about the Potomac training exercise and suggested any panic that resulted was the fault of the media, not law enforcement.
Gibbs said the "reporting was based on listening to a police scanner" and wasn't "verified" before being reported. He said media should "check before reporting" such events.
Asked if Sept. 11 was an appropriate day for such a training exercise, Gibbs said, "I tend not to question law enforcement trying to keep the nation safe."
"If anyone was unnecessarily alarmed based on erroneous reporting that denoted shots had been fired, I think everybody is apologetic of that," Gibbs said.
Coast Guard Commandant Thad Allen was at the Pentagon for the Sept. 11 remembrance ceremony this morning. Homeland Security Secretary Janet Napolitano, according to one source, was unaware the exercise was to take place.
About an hour after the scare, the Coast Guard put out a statement reading, "We are still gathering information of how this training event might have been misconstrued as an actual incident. We will conduct a thorough review of this incident."
It continued, "The best way that we in the Coast Guard can remember Sept. 11 and our security obligations to the nation is to be always ready and this requires constant training and exercise. To ensure the appropriate readiness posture we conduct training scenarios across the nation on a daily basis."
Others joined in anger about the anxiety created on a day of mourning.
"The anxiety caused by this situation on such a solemn day is extremely disturbing," Sen. George Voinovich, R-Ohio, who sits on the Senate's Homeland Security Committee, said in a statement. "I look forward to hearing from Secretary Napolitano about the decision-making process leading up to today's events. It sounds very much like the left hand didn't know what the right hand was doing."
Military Families United, an advocacy group, issued a statement as well: "Whomever commissioned this training exercise at the same time and less than a mile away from where the families of the 9/11 victims gathered to mourn should be held accountable. Their actions brought back all of the feelings for victims of 9/11 that they originally experienced 8 years ago today."
ABC News' Brian Hartman, Lisa Stark, Brian Ross, Pierre Thomas and Jack Date contributed to this report.