Refactoring is a wonderful tool when used well.
If you have well designed tests in your monolith this will be fairly easy. If not you'll want to add them. Adding them later is always more expensive but still preferable to coding and hoping.
What this is really about is that the real requirements for your project are in working code. That means you must be careful to preserve this working status as you make changes. Good tests ensure behavior hasn't changed even when structure has.
Do this slowly and carefully and it's remarkable how you can turn a design completely inside out and keep everything working.
From your comment:
That answeres one part of my question. The other was: Does it make sense to develop a system which uses both a monolithic and a microservice based architecture? - toogley
It wouldn't make sense to keep adding functionality in both monolithic and microservice styles at the same time. However, there is no reason you couldn't break off a piece as a microservice and leave the rest monolithic until you got around to breaking up the rest of it.
Each style has benefits and trade offs. By being stuck half way you wont fully have the advantages of either. But you will have the advantage that you can start working towards your goal without having to shut everything down until you're done.