God is Just.  

The Sovereign God has a law and it requires absolute justice.   Because God is love and God is just, divine justice is never cruel, but rather a necessary protection of goodness.  

Justice refers to God's actions, righteousness refers to God's character.   What He does proceeds from Who He is!

Deuteronomy 32:1-4

[1] Give ear, O ye heavens, and I will speak; and hear, O earth, the words of my mouth.
[2] My doctrine shall drop as the rain, my speech shall distil as the dew, as the small rain upon the tender herb, and as the showers upon the grass:
[3] Because I will publish the name of the LORD: ascribe ye greatness unto our God.
[4] He is the Rock, his work is perfect: for all his ways are judgment: a God of truth and without iniquity, just and right is he.

Genesis 18:20-26

[20] And the LORD said, Because the cry of Sodom and Gomorrah is great, and because their sin is very grievous;
[21] I will go down now, and see whether they have done altogether according to the cry of it, which is come unto me; and if not, I will know.
[22] And the men turned their faces from thence, and went toward Sodom: but Abraham stood yet before the LORD.
[23] And Abraham drew near, and said, Wilt thou also destroy the righteous with the wicked?
[24] Peradventure there be fifty righteous within the city: wilt thou also destroy and not spare the place for the fifty righteous that are therein?
[25] That be far from thee to do after this manner, to slay the righteous with the wicked: and that the righteous should be as the wicked, that be far from thee: Shall not the Judge of all the earth do right?
[26] And the LORD said, If I find in Sodom fifty righteous within the city, then I will spare all the place for their sakes.

What if God's nature produces a conflict within himself?

Here is a striking example: God loves man but he cannot overlook their sins because of his righteousness. So he became a man in Jesus Christ and paid the penalty for man's sin by dying on the cross. By this action His Justice was met and His love was satisfied for man.