Sūktas 14 to 18 of Maṇḍala 10 relate to the cremation of a person who has died. Most of these sūktas form a single narrative so they should ideally be read together. In sūkta 16 verse 5, Agni is being addressed, seemingly by the priest, while the body is actually being cremated. पुनर् is a separate word ('again' or 'back') that just happens to be next to 'Agni'. My translation of the whole verse is as follows -
"Agni, send back to the ancestors [he] who, offered [to you, i.e. placed in the fire], moves by [his] inherent power
Entering into life (should be आयुर् not अयुर्), let him get the remainder [of his life???]; let him go across with his body, Jātavedas"
The second line is somewhat unclear. The Hindi commentary I have interprets the second part of this as "यह मृत व्यक्ति पुनर्जीवन को प्राप्त हो" but from the context the idea seems to be that he should reunite with his body in the world of the ancestors.
I attempted my own translation of sūkta 16 verses 1-8 here.