Filter mode causing artifacts when sprites are touching

I'm playing around with new asset pack Kenney has posted and I'm trying to create landscape from tiles he created. When I import them, Filter mode is set to Trilinear and there are gaps between tiles. Those gaps are certainly not real gaps because they are also visible when tiles are overlapping. Reference image:

Then I tried changing Filter mode to Point which left me with pixelated and ugly tiles but with no gaps. Result:

As you can see, neither option is nice and I need to find another way to connect those tiles nicely. But I would like to create levels on fly from text files so using Photoshop to glue tiles together is also not an option.