Final answer:
The ultimatum from Rome during the communication with Constantinople manifested as the call for the First Crusade by Pope Urban II, who framed the Byzantine-Seljuk conflict as a religious war.
Step-by-step explanation:
The ultimatum that came from Rome after the bantering back and forth with Constantinople resulted from escalating tensions and strategic necessities felt by both the Byzantine Empire and the Western European powers. During the period of difficulty for Constantinople, one significant event was when Alexios I, one of Romanos's successors, sought assistance against the Seljuk Turks by reaching out to the popes. Expecting a mercenary force, he was met with a different response when Pope Urban II framed the conflict as a battle between religions, which led to the call for the First Crusade. This intermingling of religious fervor, political strategy, and desperate need for military support illustrated the complex dynamics between Rome and Constantinople.