Richard Barnes, who earns just over £96,000 a year, made his "throwaway" remark last week at a transport committee meeting.
Mr Barnes, who is responsible for Mr Johnson’s social justice policies, has previously spoken about how he and the Mayor are "determined to make a difference in addressing inequalities".
The Conservative made the comments at City Hall on July 14 in a discussion about the High Speed 2 rail project.
Asking about the cost of redeveloping Euston station, Mr Barnes said: "Are they like most Irish builders … saying it’s going to be roughly that [he licked his finger as if checking the wind direction]. Are we working on estimates?"
Labour Assembly member Murad Qureshi, who was at the meeting, said: "I was taken aback by the comment. Given the huge contribution made by the Irish in building London, this is particularly offensive.
"What is even more shocking, is that he made these comments as the Mayor’s lead on equality and diversity policies. He should make an unreserved apology to the Irish in London."
He added: "He’s been pretty exemplary on the subject of equality other than this. He has to accept that someone in his position making a comment like this is not acceptable."
Mr Barnes said: "If anyone was offended I will turn around and apologise but no offence was intended and I’m sure none of my Irish friends would find it offensive. It was a throwaway line. We’ve all had builders."
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