David in Psalm 139:21-22 states:
"Do I not hate them, O Lord, who hate You? And do I not loathe those who rise up against You? I hate them with perfect hatred; I count them my enemies."
It is important to remember here that God had set aside a nation for himself and at this time the enemies of David the King of Israel were also the enemies of God.
Today we have a King who is greater than David, King Jesus. His kingdom is "Not from this world". Paul also notes that:
"For we do not wrestle against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this age, against spiritual hosts of wickedness in the heavenly places." (Eph 6:12)
More specifically the prophets of God, like Elisha, were His messengers and called to a purpose that men no longer have given the Word of God is complete in the Scriptures.
I believe that this means that we no longer have a calling to curse anyone but instead to fight against spiritual wickedness. We do this by wrestling in prayer and by using the Word of God to tear down the enemies strongholds.