Should I refuse my advisor's request to write a research paper?
I suspect that the time you invest in writing any papers now will be mostly paid back because it will make it much easier to write your dissertation.
I published several papers during my PhD research, and am currently writing my dissertation. My first step was to copy the introduction from each paper into my literature review chapter, and put the body of each paper into a separate chapter of my thesis. Of course, I have to write segues and reorganise the information a bit, but that gave me a big head start on the dissertation. Of course, you'll need to check that the copyright agreement you sign with the publisher allows you to include content from your paper in your PhD dissertation (most do), and also verify that your institution allows this as well.
Another tip: If you write a paper, hang onto any material that you cut out to meet space requirements. You may want to include that material in your thesis.
Publishing journals is an important part of being a PhD student and researcher. A PhD without publication would be detrimental for your career even is it is considered to be optional by your institution.
You can't be to sure when your ongoing project will come to completion. Research results are better published as soon as they are obtained. Your advisor knows this fact. Your ought to follow your advisor's induction in this aspect. In fact, it would be even better to discuss this issue with your advisor to come to a consensus.
You should sit down and have a talk with your adviser about this. It's your responsibility to ensure you're going to graduate on time. It's also important for you to publish your work. Publishing is an important part of research and getting a PhD is learning how to do research.
How a frank discussion with your adviser about the time restrictions you have and how to balance both commitments.