Studies published in 1992 and 1997 indicate that the level of aerobic fitness of an individual does not have any correlation with the level of resting metabolism. Both studies find that aerobic fitness levels do not improve the predictive power of fat free mass for resting metabolic rate.
However, recent research from the Journal of Applied Physiology, published in 2012, compared resistance training and aerobic training on body mass and fat mass in overweight adults (STRRIDE AT/RT). When you consider time commitments against health benefits, aerobic training is the optimal mode of exercise for reducing fat mass and body mass as a primary consideration, resistance training is good as a secondary factor when aging and lean mass are a concern. Resistance training causes injuries at a much higher rate than aerobic training. Compared to resistance training, it was found that aerobic training resulted in a significantly more pronounced reduction of body weight by enhancing the cardiovascular system which is what is the principal factor in metabolic utilization of fat substrates. Resistance training if time is available is also helpful in post-exercise metabolism, but it is an adjunctive factor because the body needs to heal sufficiently between resistance training episodes, whereas with aerobic training, the body can accept this every day. RMR and BMR are measurements of daily consumption of calories. The majority of studies that are published on this topic look at aerobic exercise because of its efficacy for health and weight management.
Anaerobic exercise, such as weight lifting, builds additional muscle mass. Muscle contributes to the fat-free mass of an individual and therefore effective results from anaerobic exercise will increase BMR. However, the actual effect on BMR is controversial and difficult to enumerate. Various studies suggest that the resting metabolic rate of trained muscle is around 55 kJ/kg per day. Even a substantial increase in muscle mass, say 5 kg, would make only a minor impact on BMR.