Obviously, the answer lies somewhere in the definition of the word "cause."
"Unemployment," as a phenomenon, is a trend among millions of workers, in a variety of contexts, each with a complicated causal factor set. The number of people who gain and lose jobs every year dwarfs the total number of folks who were unemployed for that year; from that perspective, "unemployment" figures are an equilibrium, affected by fundamentals, and effects at the margin. When I say "at the margin," I mean the folks who were the last hired and fired- the ones that are affected by a company's decision to say, lay off 110 workers rather than 100. You could call them "the most employable unemployed" and the "least employable employed."
For any individual unemployed person, their previous rate of pay, their savings and assets, their skill set, where they live, the cost of moving elsewhere, the reason they left their previous job, availability of government benefits both temporary and permanent, etc. are all "causes" of their unemployment. Meta factors like consumer demand, government spending, unemployment compensation policies, etc. are still factors, but it's important to know that they are almost invisible at the individual level. I've heard it stated, and I think it's probably true, that if it weren't for statistics and newsmedia, the average person would not be able to discern the difference between 4% unemployment and 10% unemployment. They would notice local pockets of unemployment, for sure; but they would have no idea whether their local phenomena were offset by local phenomena elsewhere.
Only in the most myopic sense is unemployment "the unwillingness of a worker to accept a job at a rate offered," coupled with "the unwillingness of an employer to pay a rate at which the worker is willing to work." That said, jobless benefits obviously and axiomatically factor into that equation for each worker for whom they are available. Now, that probably doesn't change the balance of the equation for the vast majority of unemployed and employed people. However, at the margin, there will be "the most employable unemployed" and the "least employable employed" who would have taken a job but for their government benefits, or not taken a job had they had slightly more government benefits.
Having an effect at the margin undeniably "causes" an increase in unemployment. The magnitude of that change is dependent on the marginal benefit of employment to those who would be employed but for the benefits; and that is where the real tough economic analysis lies in the joblessness/unemployment benefits debate.