Rudd, however, said she did not think Johnson was laying the groundwork to challenge May.
Johnson tweeted that he fully backed the prime minister and her speech, to be delivered in Florence on Friday, but many accused him of launching a leadership bid and trying to undermine what is expected to be a more conciliatory approach from May.
I must say that I was surprised and disappointed by your letter of today, since it was based on what appeared to be a wilful distortion of the text of my article.
"It is a clear misuse of official statistics", Norgrove said in a letter to Johnson on Sunday.
He wrote that the referendum was "decisive" and said Britain must leave the EU's customs union and single market, the jurisdiction of the European Court of Justice and impose controls on borders.
Johnson included the figure in a pro-Brexit article for the The Daily Telegraph on Saturday. "She is driving the vehicle - 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". "I am here to tell you that this country will succeed in our new national enterprise, and will succeed mightily".
The Home Secretary said she did not think Mr Johnson's article was a leadership bid and said her Cabinet colleague added "enthusiasm, energy, and sometimes entertainment".
"I haven't got time for the rest of it", she said.
Damian Green, a close ally of the prime minister, told Radio 5live's Pienaar's Politics, that the timing of Mr Johnson's article "could have been better for all sorts of reasons not least the awful terrorist incident we've had".
Johnson's only comment since his Telegraph article was published was on Twitter, where he said he was "looking forward" to May's speech in Florence later this week.
"We already have a deep level of collaboration with the European Union on security matters and it is in both our interests to find ways to maintain it", Brexit Secretary David Davis said in a statement.
As part of a new treaty, Britain wants the creation of mechanisms to maintain current operational capabilities between the United Kingdom and the EU.
She said a new treaty would "lock in" existing cross-border crime-fighting and intelligence-sharing arrangements and enable the United Kingdom to remain a member of Europol outside of the EU.
He insisted Brexit would allow the United Kingdom to "be the greatest country on earth" and "our destiny will be in our own hands". We do not control them.