However, do you think it is possible to add a continuous air gap (for
example 1mm) to the iron powder cores?
If your manufacturer can manufacture it with a gap, or you can build one yourself then yes.
I know that we can add this kind of air-gaps to ferrite material, but
is it going to create a problem if we add a gap in iron powder cores?
What you really need to do is design your core for how much Magneto Motive Force (MMF) you desire to go around your core. Adding an air gap is like adding a resistor in the circuit, and limits how much MMF can flow around the core. First find the max MMF you want around the core. Find the reluctance of the core, then design your air gap to increase the reluctance of the core to your max MMF value.
There is a good guide on how to do this here: http://info.ee.surrey.ac.uk/Workshop/advice/coils/gap/index.html