A prominent Brexit campaigner in last year's referendum, Johnson also repeated the controversial claim that the government would be 350 million pounds ($476 million) better off per week once outside the EU.
Prime Minister Theresa May is set to release her Brexit plans this week.
"The Tories have a chance to step back from the brink, and back staying in the single market and the customs union - not just on a transitional basis but for the long-term to protect our economy and retain access to the biggest market in the world".
He stood by the criticism when the Foreign Secretary's aides later claimed he was "absolutely fine" with the piece. "It is a clear misuse of official statistics".
Video Boris accused of trying to undermine PM
Choosing not to withdraw the comment, Rudd said: "What I meant by that is I don't want him managing the Brexit process".
However, the foreign secretary's decision to reopen the debate was not welcomed by Cabinet colleagues including the home secretary, Amber Rudd, and first secretary of state, Damian Green.
The watchdog said the article "confused" the size of the UK's annual gross and net contributions to the EU's budget.
The Foreign Secretary revived the widely-criticised claim quitting the EU could boost NHS coffers by £350 million a week and warned against paying for access to European markets in the future.More news: Narendra Modi dedicates Sardar Sarovar Dam to nation
Mrs Rudd insisted the Prime Minister is "driving the car" and, when pressed on Mr Johnson's actions, said: "You could call it backseat driving".
The UK will say the proposed treaty will set up mechanisms that maintain operational capabilities between it, the European Union and its 28 member states, set a "high standard" of data protection and provide a mechanism for resolving disputes.
However, it caused controversy amid warnings that it did not take into account Britain's rebate from the EU.
Labour MP Chuka Umunna, who is a staunch Remainer, also blasted Mr Jonhson.More news: Bitcoin platform to stop trading end-September
Lib Dem leader Sir Vince Cable said: "I'm glad to see the independent UK Statistics Authority has the courage to slap Boris down". If the Foreign Secretary is not party to talks about Britain's changing status with Europe, and the rest of the world, what is the goal of this supposed Great Office of State? "She is driving the auto - to continue the allegory - and I'm going to make sure as far as I am concerned and the rest of the cabinet are concerned that I'm going to help her do that".
With May due to set out her vision for Brexit in a speech in the Italian city of Florence on September 22, Johnson published a 4,300-word newspaper article on September 16 that roamed well beyond his ministerial brief and, in some cases, went beyond the approach set out by the government.More news: Rising River Could Close I-75 in Florida, Complicate Evacuees' Return Home
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