Image copyright Reuters Image caption Mr Johnson met US President Donald Trump at the UN on Monday
The foreign secretary said on Monday that his article was meant to be an "opening drum roll" for the PM's speech.
"Because I was involved in that Brexit campaign, people want to know where we are going," he added.
Mrs May attempted to avoid a public row with her foreign secretary, telling reporters travelling with her on a trade mission to Canada: "Boris is Boris."
Image copyright PA Image caption Lord Hague is concerned about cabinet disunity over Brexit
Former foreign secretary, Lord Hague, writing in the Daily Telegraph, warned that disunity over Brexit could hand power to Jeremy Corbyn's Labour Party.
He wrote: "It is putting it a bit too politely to say, in the wake of Boris Johnson's article in this newspaper on Saturday, that the approach of senior ministers to the Brexit negotiations appears to lack co-ordination.
"More bluntly, it is now 15 months since the referendum, and high time that all members of the government were able to express themselves on this subject in the same way as each other, putting forward the same points, as part of an agreed plan."