TLDR; A "Yes/No" answer is impossible. While the practical answer is "refer to your local laws", if you're asking for opinion. there's alot to talk about, because legality and morality have nothing in common.
I want to laugh, not because of the question but because how I I know there is no end to the arguments on both sides of this equation.
(musing hasn't yet allowed for Youtube embedding, but please watch the 1 minute video to understand my point of view)
Do you see what's happening in the clip? Wendy Williams, American celebrity talk show host, just advocated a woman to perform what is legally a crime in the name of "woman empowerment" because "men never had control over your body".
Imagine if the roles where reversed. Imagine what would happen if a husband who wants another baby asks if it's okay to trick his wife into getting off pills and get herself pregnant. Can you even imagine that? so okay if the gender were reversed the people in the show so openly celebrate it?
While there is indeed many issues in regards to the discrimination of woman, in many cases men equally face discrimination where society favours women regardless of the situation where the man gets handed a shit steak to gobble down or else.
If a man has expressed interest to take care of the baby and has the capability to do so, why should he be denied the decision right if the woman considers abortion?
Then again, it's the woman's body, how is it moral if she does not have 100% control of it?
I am pro-choice. I believe it is a woman's right to have full ownership to her body. But at the same time I believe that consent extends beyond the few minutes of sexual intercourse.
The root of the issue however seems to be the relationship dynamic between the man and woman because if they are both in a healthy relationship and both are in sync with each other of their decision and needs, this would never have been a problem in the first place.
It is my understanding that where I live in California nobody has the legal right to oppose a woman's choice to have an abortion.
Morally it is not good to abort a child especially when you know the father and he is ready to take care of the baby.
But to your question, I don't think the father have the right to stop the woman from aborting the baby.