"As of October 5, our national recall repair completion rate stands at 38.6 percent," the automaker said. "Moreover, in high absolute humidity zones, areas believed to pose the greatest risk of inflator rupture, our recall repair completion rate is 41 percent."
More than 3.5 million defective Takata inflators have now been replaced in Honda vehicles.
It added: "But with millions of vehicles still in need of repair, we must do more."
The defective Takata airbags can deploy with too much force, spewing shrapnel at vehicle occupants. The faulty airbags have been linked to eight deaths and hundreds of injuries.
Honda dealers are "well positioned to manage incoming demand" in the recall, Honda said.
In recent months, Honda and Acura dealers in the U.S. have replaced upwards of 24,000 Takata airbag inflators on a daily basis.
Additional replacement inflators are now available from auto suppliers Daicel, Autoliv and TRW.
Honda said it is ramping up a new round of print, digital and radio advertising in several test markets to remind consumers about the Takata recall.
It is also using social media to raise awareness, including a new round of customized Facebook posts.
The National Highway Traffic Safety Administration now estimates there are 23.4 million defective Takata inflators in U.S. vehicles.
NHTSA will hold a public hearing on October 22 to discuss a possible coordinated remedy program for the Takata recall.
Edmunds says: The Honda announcement is a reminder for all consumers to check the NHTSA VIN Lookup Tool to see if their vehicle is involved in the Takata recall. If it is, it's time to get the vehicle repaired for free at an authorized dealership as soon as possible.