The Prime Minister has played down concerns that Johnson is seeking to influence her set-piece speech on Brexit, which she will deliver in Florence on Friday.
Mr Hague's comments, in an article in the Daily Telegraph, came after days of headlines about Government infighting over Brexit.
Despite the challenge to her authority, May sought to brush off the controversy during a trip to Canada on Monday, referring to his reputation for gaffes by saying "Boris is Boris".
Johnson has said he is not going to resign and said the Cabinet is united on Brexit, likening his fellow ministers to "a nest on singing birds".
The Foreign Secretary spoke to TV cameras in NY after bumping into them at a hotel lift as he returned from a jog.
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Even as tensions rise, the United States and its allies have stuck to a hands-off policy when North Korea test-fires its missiles. Mattis said the United States and Japan did not shoot it down because it did not pose a direct threat to either nation.
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Mr Johnson said: "We are working together, that is the key thing, to make sure that Britain can take advantage of the opportunities of Brexit".
Billed as the PM's most important update to the Government's position since her Lancaster House address in January, the speech is thought likely to include an attempt to break the deadlock over the UK's financial settlement.
Mr Johnson and Mrs May are both in NY, but no formal meeting between the two is planned.
Addressing one of the most contentious issues in negotiations with Brussels, he said Britain should not continue paying into the European Union budget after Brexit, even as the price of continued access to Europe's single market.
Speaking on the BBC's Today Programme this morning, prominent Remainer Clarke said the foreign secretary's "personal publicity" was an "irrelevant nuisance".
Boris Johnson must stop trying to exploit prime minister Theresa May's weakened position, a former Tory cabinet minister has warned.