Jesus did state some new laws.
Every time He declared "You have heard it said.... But I say to you"
this is a change in the understanding of the O.T. law.
This is what it means that Jesus came to fulfill -- to make more perfect.
No, not in the example you are giving above. He was correcting the "understanding" of something existing.
Otherwise He repeated many verses from the O.T.
Most notably, he quoted Deuteronomy frequently.
I understand the beatitudes to be a teaching on how Jesus would want us to behave.
Yet, they are nothing new. The concepts already existed.
<snip>
So I would say that the beatitudes are a law:
The "Sermon on the Mount" including the "Beatitudes" are based upon teachings already contained within the TaNaKh (Old Testament) and books of wisdom.
Matthew 5:3 Blessed are the poor in spirit, for theirs is the kingdom.
TaNaKh: Mishle [Proverbs] 29:23 …he who is lowly in spirit shall obtain honor.
Matthew 5:4 Blessed are those who mourn, for they shall be comforted.
TaNaKh: Tehillim [Psalms] 147:3 He heals the brokenhearted, and binds up their wounds.
Matthew 5:5 Blessed are the meek, for they shall inherit the earth.
TaNaKh: Tehillim [Psalms] 37:11 The meek shall inherit the earth, and delight themselves in the abundance of peace.
Matthew 5:8 Blessed are the pure in heart, for they shall see God.
TaNaKh: Tehillim [Psalms] 24:3--4 Who shall ascend the mount of the Lord, and who shall stand in His holy place? He who has clean hands and a pure heart…
Matthew 5:9 Blessed are the peacemakers, for they shall be called sons of God.
TaNaKh: Tehillim [Psalms] 34:14 …seek peace and pursue it.
Matthew 5:39 …but if anyone strikes you on the right cheek, turn to him the other also…
TaNaKh: Eykhah [Lamentations] 3:30 Let him offer his cheek to him who smites him…
Matthew 5:42 Give to him who begs from you, and do not refuse him who would borrow from you.
TaNaKh: Tehillim [Psalms] 37:21 …the righteous deals graciously and gives. Psalms 37:26 All day he deals graciously and lends…
That should be enough to get the idea. Thus the concepts contained in the books of wisdom are also now part of the "law"?
Know that you need God.
Understand that we live in a fallen world.
Be gentle.
Be righteous in your dealings with others.
Be merciful to all. Practice your love.
Be pure in heart so you can hear God.
Make peace, not war.
Do not deny God.
All of which was already written beforehand.
Mic 6:8 He hath showed thee, O man, what is good; and what doth the LORD require of thee, but, to do justly, and to love mercy, and to walk humbly with thy God?