Motor power rating and in-rush current
When motors are sold by themselves, not as part of an appliance, the power rating is usually the mechanical output power. In that case, the normal running current could be more than twice the current that you calculated. In a small motor, losses are high and power factor is low, resulting in higher current. That would explain while the original fuse is 3A.
You should find a way to use a fuse that is just like the original fuse.