Portuguese term (edited): (departamentos) de suma importância

'utmost' is, in general, a very good translation of 'de suma importância' but doesn't work as a modifier of 'department', 'agency', etc. Where it does work, almost always brilliantly well, is in expressions of urgency: "It is of the utmost importance that we improve medical care for the elderly."

Both 'critically important departments' (14,000 Google results) and 'crucial departments' (33,100 results) are widespread, established usage in English.

www.walkingsky.com/restless/Daily13/.../Political Ballet.pd...‎ : "politicians and their appointees to critically important departments and ... government monies, nor support that was designated to go to them ..."

earlytimeplus.com/newsdet.aspx?q=990‎ : "His work seemingly impressed the state government so much that ... before being moved out to head two critically important departments i.e. ..."

www.care2.com/.../its-not-a-good-idea-to-make-things-harder...‎ : "Senate Won't Fill Unprecedented Vacancies in the Federal Court System ... stay open, but to maintain critically important departments and programs..."

www.elpasotimes.com/ci_18330712‎ : El Paso Times. "Counties in Texas are an extension of state government. ... Even crucial departments like the Purchasing Department don't answer to ..."

youth.marsgroupkenya.org/index.php?option=com_mmedia&story...‎ : youth - OP, Prime Minister's Office To Lose Crucial Departments. "The fate of seven government departments hangs in the balance after revelations they are duplicating some functions of the chief employer of ..."

www.thestatesman.net/.../27910-dalu-attacks-state-govt...‎ : The Statesman : "He said that the 'unprecedented' incident bared the fact that the state government lacks coordination among crucial departments like administration and police..."

'departments of the utmost importance': 0 Google results
'departments of utmost importance': 5 results