Bordering on sophistry, head of government backed away from this response, ultimately to offer condolences (10)
I believe the answer is:
sympathise
'bordering on sophistry head' is the definition.
The definition suggests a verb in its base form which matches the answer.
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for sympathise that I've seen before include "Express fellow feeling" , "commiserate" .)