Military engagement

A military engagement is a combat between two forces, neither larger than a division and not smaller than a company, in which each has an assigned or perceived mission. An engagement begins when the attacking force initiates combat in pursuit of its mission, and ends when the attacker has accomplished the mission, or ceases to try to accomplish the mission, or when one or both sides receive sufficient reinforcements, thus initiating a new engagement.

As a tactical mission, the engagement is often a part of a battle. An engagement normally lasts one to two days; it may be as brief as a few hours and is rarely longer than five days. It is at this scale of combat that tactical engagement ranges of weapons and support systems become important to the troops and their commanders.

...
Wikipedia