The recall includes 344,000 Odysseys and 68,000 Elements from the 2007 and 2008 model years.
Honda said in a statement that over time, brake pedals can feel "soft" and must be pressed closer to the floor to stop the vehicles. Left unrepaired, the problem could cause loss of braking power and possibly a crash, Honda spokesman Chris Martin said.
"It's definitely not operating the way it should, and it's safety systems, so it brings it to the recall status," he said.
The National Highway Traffic Safety Administration has reported three crashes because of the problem with minor injuries and no deaths, Martin said. Honda notified NHTSA of the recall on Monday, he said.
Honda has traced the problem to the device that powers the electronic stability control system, which selectively brakes each of the wheels to keep the vehicles upright during an emergency situation.
When the device, called a "vehicle stability assist modulator," tests itself when the vehicles are started, it allows a small amount of air into the hydraulic brake lines. Over time, an air bubble in the lines can cause a loss of braking power, Martin said.
Under the recall, which Honda said it volunteered to do, the company said owners should wait to get a letter before scheduling a repair because the parts are not yet available. Letters should go out toward the end of April. Drivers who fear that they've lost braking power should have their dealer check the brakes sooner, Martin said.
The automaker is preparing a list of affected vehicles. After April 19, owners can determine whether their vehicles are being recalled by going to www.recalls.honda.com or by calling (800) 999-1009, and selecting option No. 4.