my partner suffers from depression. He attempted suicide once, ten years ago when we were friends but not in a relationship, and has experienced suicidal ideation a few times in the 8 years we've been together. I really understand. It is frightening. You cannot prevent him from doing it if that's what he decides.
But we have built a really wonderful, joyful, loving relationship together. There have been times when I've been really frightened by his mental state, but for the most part we have reached a point where we meet his depression as a united front; he tells me when he is feeling wobbly and we try to keep communicating through whatever's going on, even when he can't really speak or get out of bed.
Sometimes it has been very very hard to put myself and my fear aside to just BE THERE for him unwaveringly and without judgement; sometimes being with someone who is suffering from depression is thankless and awful and you want to scream. You need a huge reserve of personal strength. I can only say what's worked for my relationship and that's for both of us to have a responsibility to 'us', the unit: for me to be patient and gentle with him, and for him to try to recall that I am a person too, even in his darkest moments. Depression is a viciously anti-social illness but you can still keep hold of one another through it.
I just want to make sure that he is not holding the threat/possibility of suicide over you. It's one thing to acknowledge that it is there, and another to build the whole conversation around it and make it powerful. If this terror that he might have killed himself is coming only from you, then you need to find a way to deal with it; if he's well enough that might involve his cooperation, eg you agree that he answers the phone to you at X time of day, or that he checks in sometimes or whatever. If he isn't well enough you need to find the strength within yourself to not wrap yourself up in knots and demand things of him that he can't deliver.
However, if it's something he uses to control the situation then protect yourself and get the hell out. Nobody needs to be with someone who uses their MH as a weapon. It's definitely not your responsibility to keep him safe, either way; at most your responsibility extends to maintaining a healthy relationship without exhausting yourself, and that's as much for your benefit as his. You do not need to feel trapped there because of his MH.
(I'm not saying that's how you feel, I'm just saying it's a potential pitfall. Most people with MH problems do not seek to milk them.)
Good luck. I promise it can be wonderful.