Mr Johnson, asked by reporters on Dec 7 if he had intervened in the evacuation last summer, called the suggestion “complete nonsense”.
Downing Street distanced Mr Johnson from involvement in the decision on evacuating the Nowzad animals, when asked about the claims on Wednesday.
The Prime Minister’s official spokesman said: “It remains the case that the Prime Minister didn’t instruct officials to take any particular course of action.”
But Dominic Dyer, who led the political lobbying campaign from the UK for Nowzad to be evacuated, said Mr Johnson’s refusal to acknowledge his role in the evacuation had “tarnished” the campaign.
Mr Dyer said the emails published by the committee “vindicated” what he had previously said and argued that the Prime Minister could be “very proud of giving support to this as a humanitarian rescue mission”.
“I’m not certain why he didn’t feel he could explain his involvement in August at the end of this operation,” he said.
“I don’t know why, and I don’t know why this was allowed to turn into such a big political football, for the Ministry of Defence to fall out with the Foreign Office and for Downing Street to say it had no role in it.
“It has tarnished what has been a very important operation that had huge public support, and I think that’s a sad indictment of our political system at the moment, which the Prime Minister presides over, to be quite frank.”