Toyota and Honda might have to reduce output of their popular models.

Toyota and Honda could be forced to cut production of their most popular models as inventory levels continue to rise, a new report finds.

According to a new report published by RBC Capital Markets, the Toyota Camry and Honda Civic are at risk for production cuts due to higher-than-usual inventory levels. The Camry and Civic were the only two cars out of the top 16 best-selling nameplates in the United States that were listed as risks for reduced output.

Inventories of the Toyota Camry are currently running about 15-days higher than typical levels, while Honda dealers have an additional 25-day supply of the popular Civic compact.

"Toyota is pulling out all stops to sustain its No. 1 market position against a slew of new competition," the reports author, Joseph Spak, said, according to Automotive News. "We continue to see downside risk to production schedules for the Civic line as inventories remain well above historical levels."

Both the Camry and Civic posted sales gains in June, but the nameplates' sales are down 2.9 percent and 2.4 percent, respectively, for the year.

Meanwhile, the Detroit three automakers are ramping up production in order to keep pace with booming demand. During the first six months of 2013 all three domestic automakers increased their U.S. market share, a feat that hasn't happened for the last 20 years.