I, too, have pondered this question for quite some time. I've come to the conclusion that the answer is no. Christ never gave any such command or commission. The closest anything comes in the NT is to invite others to repent and be baptized, but this is to fulfill the commission to make disciples and baptize them.
The next question is: are ALL Christians given this commission? This leads to a discussion of apostles and disciples. The word "apostles" means literally "sent forth ones". All apostles are also disciples, but not all disciples are also apostles. Thus, it's worth noting the commendation Christ gave to the congregation in Ephesus in Revelation 2:2:
‘I know your deeds, and your labor and endurance, and that you cannot tolerate bad men, and that you put to the test those who say they are apostles, but they are not, and you found them to be liars.