Which offensive task focuses on pursuing a fleeing enemy following an engagement?

The offensive task that focuses specifically on pursuing a fleeing enemy following an engagement is referred to as a pursuit. This tactic is employed to exploit the enemy's disorganization and to maintain momentum after a successful attack, with the goal of completely neutralizing their ability to regroup or escape.

A pursuit typically begins after an enemy has started to retreat under pressure, allowing friendly forces to engage them and further disrupt their withdrawal. This operation aims to prevent the enemy from establishing a new defensive position and to capitalize on their lesser combat capability during a retreat.

Understanding this, the distinctions from other options become clearer. Movement to Contact is aimed at finding and engaging the enemy, rather than pursuing them; attack refers to a focused engagement with the enemy to seize terrain or destroy enemy capabilities; and defense involves holding positions against enemy attacks rather than actively pursuing them. The pursuit, therefore, is uniquely defined by its objective of chasing down a retreating foe and is critical in maximizing the effectiveness of offensive operations.