Contradiction with Matthew 5:44
Contradicts by instructing to love your enemies, whereas Psalms 18:37 speaks of pursuing and overtaking them.
Matthew 5:44: But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you;
Contradiction with Romans 12:19
Contradicts by teaching not to seek personal vengeance but leave room for God's wrath, unlike the pursuit described in Psalms 18:37.
Romans 12:19: Dearly beloved, avenge not yourselves, but [rather] give place unto wrath: for it is written, Vengeance [is] mine; I will repay, saith the Lord.
Contradiction with Proverbs 25:21-22
Advises feeding and giving drink to your enemy, contrary to the action of pursuing enemies seen in Psalms 18:37.
Proverbs 25:21-22: If thine enemy be hungry, give him bread to eat; and if he be thirsty, give him water to drink:
Contradiction with Luke 6:27
Encourages doing good to those who hate you, unlike the pursuit to overtake enemies in Psalms 18:37.
Luke 6:27: But I say unto you which hear, Love your enemies, do good to them which hate you,
Contradiction with 1 Peter 3:9
Advises not to repay evil for evil, which contrasts with the active pursuit of enemies mentioned in Psalms 18:37.
1 Peter 3:9: Not rendering evil for evil, or railing for railing: but contrariwise blessing; knowing that ye are thereunto called, that ye should inherit a blessing.