It has emerged that on his first day as the chairman of the Metropolitan Police Authority on Wednesday, Mr Johnson told Sir Ian the force needed fresh leadership.
She reacted angrily to the way the resignation had been handled and suggested Mr Johnson did not understand the nature of the role of commissioner.
Conservatives have criticised Ms Smith for repeatedly backing Sir Ian but Mr Johnson described talk of a plot to oust the commissioner as "completely barking", saying there was "no party political element to this."
Mr Johnson said: "I came to this conclusion after a great deal of thought and after consulting many, many people.
"I felt it was an opportunity for someone else to give stability and new leadership and greater operational effectiveness to the Metropolitan Police."
Shadow home secretary Dominic Grieve said Mr Johnson had not forced Sir Ian to resign - nor had he the power to do so - but he had indicated his lack of confidence in the commissioner. It was a sentiment he understood, Mr Grieve added.
Ms Smith told BBC's Question Time that party politics should be kept out of the matter.
Lord Mackenzie, a former president of the Police Superintendents' Association, said the manner of Sir Ian's departure raised a number of questions and it was important not to "politicise the police".
If the Mayor of London - of which ever party - had a veto against the appointment of the commissioner, it would put us on "very dangerous ground," he added.
However, Lib Dem home affairs spokesman Chris Huhne said the resignation was "long overdue".
APPOINTING A COMMISSIONER
Shortlisting by Home Office officials and MPA chair
Candidates interviewed by MPA panel, who give the home secretary their recommendations
Home secretary interviews candidates and asks mayor's views
Home secretary must 'have regard' to mayor and MPA's views before making recommendation to the Queen
Joint announcement by Home Office and MPA
Source: Metropolitan Police Authority (based on the previous appointment)
Sir Ian's tenure as head of Britain's biggest police force started confidently with reforms including neighbourhood policing and a more diverse workforce, and he has presided over falling crime in the capital.
But he has been dogged by a string of controversies, including the shooting dead by police of Brazilian Jean Charles de Menezes, who was mistaken for a suicide bomber.
It later emerged he had recorded a telephone conversation with the attorney general without asking his permission.
In 2006, Met officers shot and injured a man while arresting two brothers who were later cleared of involvement in terrorism.
Recently, Sir Ian has faced criticism over the racism row involving the Met's most senior Asian officer Tarique Ghaffur.
And Metropolitan Police Authority auditors are in the process of examining Scotland Yard contracts given to consultancy firm Impact Plus, run by a friend.
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