In Henry IV, part 1, King Henry IV refuses to ransom Mortimer because he considers Mortimer a traitor who is siding with the rebels.
Edmund Mortimer, Earl of March, is a potential dangerous rival. Mortimer is the person that Richard II had designated as heir to the throne. As such, he is a rival to Henry because the king took the throne from Richard rather than inherit it. Likewise, Mortimer is a threat to Henry’s son and heir, Hal.
In act 1, scene 1, Henry learns from Westmoreland that Mortimer was taken prisoner. While fighting with Henry’s forces against Owen Glendower of Wales, Mortimer was captured by Glendower. Moreover, a thousand of Mortimer’s men were killed. Henry suspects Mortimer of willingly going with Glendower—a suspicion that will later be supported when Mortimer marries Glendower’s daughter.
In scene 3, Henry negotiates over prisoners with Hotspur (the young Henry Percy), who has taken many Scots. Henry not only refuses to ransom Mortimer, who is Hotspur’s brother-in-law, but he grows furious when Hotspur tries to defend the earl’s actions. Henry completely shuts down discussion of prisoners and forbids anyone to speak further about Mortimer.