Mrs Rudd, who campaigned for the Remain side in the European Union referendum, said she had been too busy dealing with the Parsons Green Tube attack to read Mr Johnson's piece and questioned the timing of its release.
Mr Johnson's 4,000-word Brexit article in the Daily Telegraph at the weekend drew criticism among some in the party and fuelled speculation that his future in the Cabinet may be in question.
Mr Johnson's announcement came hours after 29 were injured by a Tube bomb at Parsons Green station.
Teenager arrested in connection with London bombing
The number of those hurtcould have been much higher and the severity of their injuries much worse had the bomb fully detonated. The Department of Foreign Affairs has confirmed that an Irish person was injured in Tube bomb attack in London yesterday.
The Telegraph reported that Whitehall sources had said neither the Prime Minister nor the Chancellor were aware of Mr Johnson's article prior to its publication.
But the arrangements should be "versatile and dynamic enough" to allow countries to respond to changing threats, it will say, and there must also be provision for dispute resolution.
"As we prepare to leave the European Union it is therefore vital that we agree a new way to ensure continued security, law enforcement and criminal justice cooperation", she said.
Johnson argued that the United Kingdom should not pay to access Europe's single market for goods and services after Brexit, countering an idea suggested as possible by Chancellor of the Exchequer Philip Hammond and Brexit Secretary David Davis. "Mrs May must spell out now how this will be paid for or stand condemned for once again trying to mislead the British public".
Global rugby family celebrates IOC Olympic Games programme decision
One concern for Paris is that its bid was based on the sports in the 2016 Rio Olympics. Deliberately we had the Games in 1932, and 1984 as well.
He predicted Britain will succeed in its new national enterprise, adding: "and will succeed mightily".
Home Secretary Amber Rudd reaffirmed her support for the Prime Minister. "I know what an irrepressible enthusiast (Johnson) is about Brexit, and what he's done is set it out there, I think it's absolutely fine, I would expect nothing less from Boris", Rudd said on the BBC's Andrew Marr show.
He said the country would be "immensely healthier" with its destiny in its own hands - "And yes - once we have settled our accounts, we will take back control of roughly £350 million per week". The holder of Foreign affairs does not even mention possibility of a transitional period after Brexit, that will surely be storyline of Theresa May in a speech in Florence.
Theresa May's Government over Brexit and cut the ground from beneath the Prime Minister's authority. Last October he declared Britain's approach to the Brexit negotiations was "having our cake and eating it".
Outrage over ending the dreamers program
And so they've essentially been living as Americans in every way except having citizenship. Of course, immigration is a top issue for Texas Representative Joaquin Castro, a Democrat.
- Barcelona switch transfer targets from Philippe Coutinho to Liverpool teammate Sadio Mane
- ISIS Convoy Joins Terrorists in ISIS-Held Syria
- Interpreter Mostly Signed Nonsense During Irma Briefing
- Hamas says it accepts reconciliation demands
- Two Militants Killed in J&K as Army Foils Infiltration Bid
- Salman Khan receives Global Diversity Award at Britain's House of Commons
- United Nations refugee agency 'shocked' by killings in eastern DR Congo
- Restoring electricity a priority as Trump visits Florida
- Merkel urges quiet diplomacy to resolve Qatar crisis
- Trump helps volunteer efforts in hurricane-ravaged Florida