The confrontation came during the Mayor's monthly phone-in show on LBC 97.3 - thought to be only the second time the two men have spoken.
The dispute over ticket office closures was deadlocked tonight with millions of commuters almost certain to be caught in the crossfire.
London Underground says services will be affected from around 9:30pm on Tuesday 4 February.
An accident in which a Tube traveller was dragged along a platform after her scarf caught in a train door is being officially investigated.
The woman, whose scarf was wrenched off by the train, suffered back and head injuries in the incident at Holborn Underground station in central London.
Arriving at Holborn she had moved towards a Piccadilly line train but stopped as she realised the doors were closing.
The Rail Accident Investigation Branch (RAIB), which is looking into the incident, said: "As she stopped, the end of the scarf that she was wearing continued to swing towards the train and became trapped between the closing doors.
"The train operator was unaware that the scarf was trapped in the door and after confirming that all doors were closed, started to move the train into the tunnel.
"The passenger was dragged along the platform as the train started to move. The station assistant tried to help the passenger by holding on to her and they both fell to the ground. This resulted in the scarf being forcibly removed from the passenger's neck and carried into the tunnel by the train."
The RAIB went on: "The passenger suffered injuries to her neck and back and was taken to hospital; she is now recovering."
The RAIB says an investigation will now seek to understand the sequence of events and examine the arrangements in place for the safe dispatch of trains from London Underground stations where station assistants are provided on the platform,
New figures released by Transport for London have shown that there are more than 7.5 million transactions at London's Tube Ticket Offices every year.
They also reveal that between 2010 and 2013 there was a 28% drop in transactions at Tube ticket offices.
A row between unions and TFL over the closure of tube ticket offices led to a series of recent strikes across the network.
– Detective Constable Carl Wayte, investigating officer
“The victim, a 14-year-old boy from Newham, accidentally stood on a man’s foot on a 103 bus.
When the bus stopped, the man followed the schoolboy into Dagenham East station and punched him in the head.
The boy fell to the ground and was left unconscious, suffering bruising and a cut to his face.
This was a shocking and callous assault that left the young victim needing hospital treatment.
I’m urging anyone who recognises the man pictured, or has any information that could assist officers with the investigation, to please contact us.”
British Transport Police are appealing for the public’s help after a teenage boy was left unconscious following an assault.
The incident happened at around 4.50pm on Wednesday, 12 February at Dagenham East Underground station.
The 14-year-old victim, whose family are too afraid to name him, reportedly stepped on the man’s foot accidentally on a bus while joking around with a friend after school.
Despite receiving an apology the man followed the boy and confronted him before punching him in the head. The teenager fell to the ground and was unconscious on the platform at Dagenham East station for 20 minutes.
Anyone with information is asked contact British Transport Police on 0800 40 50 40, or text 61016, quoting incident reference LUA/B6 of 18/02/14.
Alternatively call the independent charity Crimestoppers anonymously on 0800 555 111.
– Phil Hufton, London Underground's chief operating officer,
Hundreds of our staff volunteered to help keep London moving during the recent pointless industrial action called by the union leaderships.
In recognition of doing this over and above their day jobs, staff who volunteered will receive a voucher for £25 by way of a thank-you.
Transport Salaried Staffs Association General secretary Manuel Cortes said it was an example of "gesture politics" by London Mayor Boris Johnson, adding:
"Instead of wasting public money on grandstanding gimmicks, he would be better of focusing on how he caused the dispute in the first place, namely his reckless plan to close all 260 Tube ticket offices.
"Before the walkout, he said he would keep services running with an army of 1,000 volunteers. On the day, the service was at a virtual standstill because only a few hundred actually turned out on the day.
"Now he is using public money on another futile gesture aimed at raising his standing in the Tory party."
The Transport Salaried Staffs Association said the volunteers, who were Transport for London employees, were paid £25 for an eight hour shift plus a further £25 if they worked two shifts over the two-day stoppage over ticket office closures earlier this month.
The union said the total cost would be over £22,000 if it was true that 950 staff volunteered to be on duty during the strike.
The managing director of the London Underground has said that he wants the next generation of Tube trains to echo the style of the Boris bus, according to the Evening Standard.
The newspaper reported Mike Brown saying he was "unashamedly" branding the rains as the New Tube for London.
Full details of LU’s £16 billion order for almost 200 new trains for the deep-level Central, Bakerloo, Waterloo & City and Piccadilly lines will soon be published, with bidders expected to include Bombardier and Siemens as well as Hitachi and Spain’s CAF.
– Spokesman for David Cameron
Bob Crow's strike is plain wrong and Bob Crow should call it off rather than inflict misery on hard-working families in London.