In many opening hails, Starfleet Captains often say they represent the UFP. They make the initial contact then once it goes further the diplomats and politicians take over.
Starfleets primary mandate is to explore and make contact with new civilisations, if they don't have the authority to meet with alien leaders then they're operating with their hands tied behind their back.
Commander Austin Harris, First Officer, Deep Space Nine (by FltCpt. Bossco)
8.01 - Darkest Before Dawn
(Chapter 8 added, 12/09/2015)