Which pharmacological agent would increase the incidence of first-degree atrioventricular heart block?

Digitalis is the correct answer because it is known to enhance vagal tone, which slows down conduction through the atrioventricular (AV) node. This effect can lead to an increased incidence of first-degree AV block, characterized by a prolonged PR interval on the electrocardiogram. The mechanism involves the action of digitalis on the heart, where it increases intracellular calcium levels, thereby modifying the conduction properties of the cardiac tissue, particularly affecting the AV node.

Other pharmacological agents listed do not have this specific effect on AV conduction. Anticoagulant agents primarily prevent clot formation and do not influence the conduction system directly. Diuretics help manage fluid balance and hypertension but are not associated with AV node conduction abnormalities. Mucolytic agents assist in clearing mucus from the airways and do not impact the electrical conduction within the heart. Thus, digitalis stands out as a drug that can specifically increase the likelihood of developing first-degree AV block.