Johnson's article reignited speculation that he would challenge May for the leadership of the Conservative Party.
Rudd, however, said she did not think Johnson was laying the groundwork to challenge May.
"I think that he, like I, supports the Prime Minister at this difficult time as we try to conclude the negotiations with the EU," she said.
May's deputy, Damian Green, also weighed in, saying that Johnson had written a "very exuberant" article but it is "absolutely clear to everyone that the driver of the car in this instance is the Prime Minister".
"It is the job of the rest of us in the Cabinet to agree on a set of proposals and get behind those proposals and get behind the Prime Minister," Green told BBC TV.
Johnson had written in the Daily Telegraph that Britain would not pay to access European markets in the future. Once out of the EU, the country should borrow to invest in infrastructure, reform the tax code and set immigration levels as it sees fit, he said.
A prominent Brexit campaigner in last year's referendum, Johnson also repeated the Brexit campaign claim that the Government would be £350 million a week better off outside the EU.
Government officials criticised Johnson for repeating the claim, saying the figure does not take into account the funding Britain receives back from Brussels.
David Norgrove, of the UK Statistics Authority, said he was "surprised and disappointed" that Johnson was still quoting a figure that confused gross and net contributions.
"It is a clear misuse of official statistics," Norgrove said in a letter to Johnson today.
Reacting to the furore his article had generated, Johnson tweeted: "Looking forward to PM's Florence Speech. All behind Theresa for a glorious Brexit".
- Reuters, AAP
HOW MUCH DOES BRITAIN GIVE THE EUROPEAN UNION?
- UK made net contribution to EU of roughly £156 million a week in 2016/17
- Treasury figures show total amount for 12 months to March 2017 was £8.1 billion, the lowest level for five years
- UK's gross contribution to EU budget in 2016/17, before the application of the rebate, totalled £16.9 billion or around £325 million a week
- But Treasury pays UK's contributions to EU after deducting value of rebate
- Rebate in 2016/17 was £4.8 billion. Subtracting this from gross contribution gives £12.2 billion. EU's payments to UK public sector gives final figure of £8.1 billion, or about £156 million a week
- Precise amount of money the UK sends to the EU is difficult to calculate because EU payments made directly to private sector, such as universities and research organisations, not included in Treasury figures and not reflected in estimate of £156 million a week
- House of Commons Library briefing paper says UK organisations receive around £1 billion to £1.5 billion a year directly from European Commission, including funding for research and innovation as part of Horizon 2020 program and money for education, training, youth and sport through Erasmus+ scheme.
- PA, AAP