The answer of this post clarifies also this related question:
Water on Mars and Earth
If water on Earth came from meteorites, why doesn't Mars have
First off, that's a conjecture regarding the origin of the Earth's
water rather than a known fact. A few times a year or so, a new
journal article will appear that argues that the Earth's water is
primordial, then another arguing that it came from comets, then yet
another arguing that it came from asteroids.
If the Earth's water is mostly primordial, most of it is over 4.5
billion years old. If it came from asteroids or comets that collided
with the Earth after the Earth had formed, it's still very, very old.
Regardless of the source, almost all of the Earth's water has been
here for at least 3.8 billion years old, since the end of the late
Mars and Earth are both rocky planets. If the water was there, at Mars or at the Earth on Archaic, then I guess degassing of Mantle was more quick than I thougth and what my hydrology teacher told us had not a lot of sense. "Regardless of the source", so then water came from both sources but probably meteorites are not the main source.