The phrase "solemn duty" means a very serious responsibility or task that must be taken seriously and approached in a respectful manner. Full definition
Because the right to life is the most fundamental of all rights, working diligently to achieve No Kill is the most solemn duty of any organization that claims the mantle of animal welfare or animal rights. (nathanwinograd.com)
Assemblyman Billy Jones (D - Chateaugay) said helping craft the state budget is one of his most solemn duties. (suncommunitynews.com)
In the context of these formidably solemn duties, it is not obtuse to say that Independent Counsel was, in fact, representing the state in the Douglas Inquiry. (slaw.ca)