Andrew Fisher, head of policy and the author of the party’s last manifesto, is said to have walked out last Saturday.
The Sunday Times reports he denounced Mr Corbyn’s team for their “lack of professionalism, competence and human decency” in a memo seen by the paper.
Mr Fisher also reportedly said he was sick of the “blizzard of lies and excuses”, and claimed a “class war” had gripped the upper echelons of the party.
Asked about Mr Fisher's comments that he was sick of the "blizzard of lies" within Mr Corbyn's team, the leader of the opposition said: "I think he said that because he was extremely distressed at that point about whatever was going on in discussions within the office at that moment."
Mr Corbyn told BBC's The Andrew Marr Show Mr Fisher "is working with us for the rest of this year - he will be here for the general election campaign, he is as we speak... downstairs".
Asked about the resignation of one of his closest aides, Mr Corbyn said: "He is wanting to leave in order to spend time looking after his son and being with his wife and his family - because this is a very stressful and very full-on job.
Mr Fisher also warned that the party would not win the next general election.
But Labour's shadow home secretary Diane Abbott strongly disagreed with that, citing the 2017 general election as an example of how Labour can do well.
She told ITV News: "I campaigned in the 2017 general election and people like you (the media) said we were going to be smashed, in fact, we had one of our best results for a long time."
When reminded that Labour lost the election, she said: "Yeah, but we had a much better result than people expected."
Following his appearance on the programme, Mr Corbyn refused to answer questions from one of ITV News Political Correspondent on his aide's resignation.
A Labour source told ITV News Mr Fisher's commitment to the party and Mr Corbyn shows how strongly he must have felt to resign.
"Do not underestimate how loyal Andrew is.
"If he’s walking then that’s a damning indictment on the leadership’s operation," the source said.
Mr Fisher's resignation will be a significant blow to 70-year-old Mr Corbyn, who, it is claimed, may also stand down because he feels under “incredible pressure”.
A Labour source said: “We don’t comment on staffing matters.”
There was a grassroots plot by an ardent Mr Corbyn supporter to abolish the role of deputy leader, a position currently held by Tom Watson.
That potential controversy was temporarily put to bed by the leader, who called off a vote on whether to remove the role, but the wounds are still fresh.