Are those two concrete slabs just laying on dirt or are they attached to anything?
If they are just laying there, which is what it looks like, putting goo between them is not going to work because they will move around due to changes in temperature and work loose.
Assuming the blocks are free standing, the natural thing to do is just leave them as is.
If you are determined to get a perfectly sealed fit, the blocks need to be attached both to each other and to the stoop. One way to do this:
- Remove the two blocks and set them aside and check out the foundation of the stoop.
2a. If the stoop is just laying on dirt, like the blocks (doh), then dig under the stoop all along its length until you have at least 6 inches of overhang, then put down an inch of gravel, then two inches of concrete, and finally a thin mortar bed. Before the mortar bed sets, put the two blocks back on top and the mortar bed will hold them firmly to the stoop and both will be joined to the concrete mini-foundation.
2b. If the stoop has a good foundation (going below the frost line 4 feet down into the earth), then you are going to need some kind of bolt system at the very minimum. The idea here is the same as 2a except that the mini-foundation will be poured over bolts or rods that are driven into the stoop, thus joining the two together.
- Either way make sure that the new mini-foundation is drained. You need to have gravel underneath and a pipe of some sort leading from the gravel to wherever. By the way, water flows DOWNHILL, so that pipe needs to be sloped down and it needs to keep going down.
Obviously, as you can see, all of this is a lot of work. The bottom line is: no foundation, no seal. This is because without a foundation stuff will move around. If you just throw pavers on dirt, they are not going to be sealable in a climate which has below freezing temperatures.