Most bunnies don’t like to be held or carried, and arms coming into a cage can be scary to a rabbit, so it would be better if your rabbit came out of the cage on his own. What is the opening like in his cage? Is it small? Does it not open all the way to the cage floor level? Is the cage itself elevated, which would mean that the bunny would have to jump down? If the cage or cage door opening is not at floor level, you may have to put some kind of ramp on it, to make it connect more easily with the floor.

Have you tried luring him out with food? If he is old enough to be on veggies, you could try luring him out with a favorite veggie, or a little piece of fruit.

Have you been sitting near the cage on the floor with the cage door open? That might make a bunny curious, and make him want to come out and explore or check you out. Or conversely, he may be more willing to come out of an open cage if no one is hovering over him or near him.

Without knowing what kind of cage he is in and what the opening looks like, it’s hard to give the best advice. Rabbits can be scared at first and not want to come out of their cage for a few days, but after more than 2 weeks, it seems like he would want to come out, and he does need adequate out of cage time daily for play and exercise.

Hi there, welcome

Sometimes buns who have never been out of a cage can be pretty timid. You can make a ramp or steps using a piece of wood covered with a towel, or even some small cardboard boxes.

It can also help if bun feels safe when they do come out. So, put out lots of hiding spots in the play area can help. You might even want to enclose an area of the room with a pen, and leave that area open to him all the time. He will eventually come out to explore. (This would prob be a nice set-up for him anyway, as most bunny cages are too small).

Awww congrats on your new addition. My cage has a slide door and the bottom ledge where it slides is only about 2 inces off the ground (it just sits in the plastic bottom) and none of my rabbits have needed a ramp to get out.
It’s hard to tell from this photo, but I hope this helps you see what I mean. 

(To the right of where they are is where the cage slides open…. This cage is smaller than I would like, but it was just for bonding – they now have the run of the whole area where the see the bunny outside the cage)

If its higher than that then yes, he may need a ramp or something to help.
But I agree with the others, most bunnies don’t like to get picked up (or they are ok with it when they are babies and then grow out of tolerating it) they see hands coming from above like a bird of prey.
Try to always bring your hand in from the side when you do eventually try to pet him so that he can see you hand coming.

I would try to leave the cage open for hours – maybe don’t hang around where he can see you close (but where you can still see him if he hops out) and then once he gets used to hoping out on his own then start siting there.

You have got good advice from others already. I just wanted to add that it depends a bit on the age of the rabbit, whether it will be upset by being lifted/carried. Very young rabbits often don’t mind being carried. Then they hit puberty, and after that, they as a rule do no longer appreciate being carried or lifted.

I think what you’re doing is good. i had a rabbit that clearly hadn’t been accustomed to any kind of free roaming – it took him a whole year toventure further than about a yard from his safe spot under the coffee table. it was like he didn’t know what to do with lots of space. He was a fully adult rabbit and had probably been caged always. Anyway, he developed into a very social and cuddle-loving rabbit. He always had cardboard hidey houses and tunnels (cat tunnels are great for buns) and he could always withdraw to under the coffee table if he wanted to – but he withdrew less and less. He was what you’d call a slow learner, it took him years to figure out a treat ball for example. But he continously evolved, or how to put it. It was very heartwarming and interesting to get to be a part of this process.