Zelensky was speaking after accusing Russian troops of carrying out extra-judicial killings in the town of Bucha west of the Ukrainian capital, Kyiv.
Former Russian President Dmitry Medvedev said the reports of civilian killings in Bucha were "fakes" aimed at discrediting Russia. Moscow said it would present "empirical evidence" to a meeting of the United Nations Security Council on Tuesday proving its forces were not involved.
"All of us, including myself, will perceive even the possibility of negotiations as a challenge," Zelensky said in an interview with Ukrainian journalists broadcast on national television.
"The challenge is internal, first of all, one's own, human challenge. Then, when you pull yourself together, and you have to do it, I think that we have no other choice."
He said the events in Bucha were unforgivable but Ukraine and Russia should take the difficult option of pursuing talks, and signalled that Moscow should recognise what its troops were alleged to have done.
The Russian news agency Interfax cited a deputy Russian foreign minister as saying talks were continuing via video link.
Asked whether he and Putin would hold direct talks, Zelensky said it was possible this would not happen but gave no details.