This can be confusing.
"Need" can be either a noun or a verb.
"Necessary" is an adjective.
"Necessity" is a noun and it is used much less frequently.
You could write any of these:
No, it is not necessary.
No, it is not needed.
No, it is unnecessary.
Or OK but less common.
No, it is unneeded.
No, there is no need.
No, it's not a necessity.