May, Clarkson's co-presenter on the BBC motoring show, suggested those who sent the online abuse "do the world a much bigger favour by killing yourself".
"Obviously I don't actually want people to kill themselves but, really, we don't want them as fans," May added.
Perkins quit Twitter earlier this week, following the abusive tweets.
"I am off Twitter for a bit," she tweeted on Tuesday, signing off: "Love and peace."
The presenter, who hosts BBC One's The Great British Bake Off, tweeted that some of the threats she had received included someone who "suggested they'd like to see me burn to death", while her timeline "has been full of blokes wishing me dead".
She described the suggestion that she was taking the Top Gear job as an "utterly fabricated story".
Clarkson was dropped by the BBC in March after a "fracas" during which he punched producer Oisin Tymon.
Perkins was among several names being speculated over as possible replacements for Clarkson.
Last week she was announced as being the bookmakers' favourite to replace Clarkson.
Bookmakers Coral said she was the front-runner for the job, followed by Dermot O'Leary and then Jodie Kidd.
Perkins fronts several other TV shows, including programmes on travel and the Edinburgh Festival on BBC Two and a Sky Atlantic Game of Thrones live discussion spin-off called Thronecast.
May is currently preparing to tour a Top Gear spin-off around the UK alongside Clarkson and fellow co-host Richard Hammond.
There has been no further announcement as to whether he and Hammond will continue to front the BBC show following Clarkson's departure.
Presenter James May has condemned those who sent death threats to Sue Perkins over reports she was replacing Jeremy Clarkson on Top Gear.