Downing Street dismissed the comments and insisted Mr Johnson will stand down when a new Tory leader is in place
The peer is running a campaign to give Conservative Party members a vote on whether to accept Mr Johnson’s resignation as Tory leader.
But Downing Street responded by insisting Mr Johnson will leave the post when a new Tory leader is chosen in September.
A Number 10 spokeswoman said: “The Prime Minister has resigned as party leader and set out his intention to stand down as PM when the new leader is in place.”
Lord Cruddas told the Daily Telegraph: “There was no ambiguity in Boris’s views. He definitely does not want to resign. He wants to carry on and he believes that, with the membership behind him, he can.”
The peer added: “Boris thanked me for my ‘Boris on the ballot’ campaign. He said he was enjoying following it and he wished me well. He said he could understand the membership’s anger at what had happened. He said that he wished that he could carry on as Prime Minister. He said he does not want to resign.”
The Telegraph said Mr Johnson, when asked by the peer if he would “wipe away” his resignation immediately with “a magic wand”, reportedly replied: “I would wipe away everything that stops me being PM in a second.”
Lord Cruddas, who said 10,000 party members have backed the campaign, added: “He wants to carry on to finish the job. He wants to fight the next general election as leader of the Conservative Party.”
Mr Johnson, in his final appearance at Prime Minister’s Questions, declared “mission largely accomplished, for now” before signing-off by telling MPs: “Hasta la vista, baby.”
The Spanish term “hasta la vista” translates to “see you later”, but “hasta la vista, baby” is the catchphrase of Arnold Schwarzenegger’s cyborg character in the 1991 movie Terminator 2: Judgment Day.
Mr Johnson’s valedictory comments left the door open for a possible comeback, with the Terminator also known for the catchphrase: “I’ll be back.”
Conservative former minister Chris Philp, asked about the remarks by Lord Cruddas, told Channel 4 News: “That ship has sailed. We have a process which we have gone through. The Prime Minister chose voluntarily to resign, that was accepted by everybody. We have run a process in Parliament to select those final two candidates.
“He resigned, for reasons he will know about. He did that voluntarily, under pressure, but voluntarily.
“We are now going to elect a new leader. That process is going to carry forward.
“And on this point about Lord Cruddas’ petition, I would just urge people to disregard that. It’s a sideshow, and what I would certainly say, when people get their ballot papers, mark a vote for one of the two candidates, don’t spoil your ballot paper by writing anything else, if you do that, your vote won’t count.”
Conservative MP Andrew Bowie (West Aberdeenshire and Kincardine) told the same programme: “This Lord Cruddas’ petition is a sideshow, it should be given no attention whatsoever, we are focusing on the future.”