First off, congratulations on your daily runs of 4km! Staying consistent with your running is truly the secret to building strength and getting faster and gaining endurance, so if you are consistently running 4km each day or most days of the week, you will see that it is easy for you to start increasing your mileage.
How many miles you "should" be running in a day is dependent on your individual running goals. There is no golden number of miles that will translate to success until you have actually defined what success is to you. That means, if your goal (or your measure of "success") is to complete a 5k or 10k, then you will need to work your way up to steadily run those distances. But if your goal is speed for those races, meaning you want to compete in a 5k or 10k and run your absolute best time possible, then not only will you probably need to be able to run a bit farther than those distances, but you will want to incorporate speed and other forms of workouts into your routine.
If gaining running strength is your goal - which it sounds like it is - then what you have read is correct. Increasing your speed and distance will definitely make you a stronger runner. To get stronger than you are now, first aim to start increasing your mileage past your 4k-a-day runs. Slowly incorporate more miles and increase by one to one-half a kilometer each time you go for a run. So for example, if you run four days a week, start the week off with a 4k run, then go up to 5k, then 5.5k then 6k. Once you have established a solid distance base (i.e. you can run a 10k without stopping), then focus on increasing your leg-turnover, which translates to faster paces and running times. And finally, make sure you are fueling your runs properly! Get adequate fats, protein, and carbs into your diet to give you stamina and be sure you are drinking plenty of water. Do all of this consistently, and you will start to see significant gains in your running strength!