Crow, the general secretary of the Rail, Maritime and Transport Workers Union (RMT), said his union's negotiators were still in talks with officials from Transport for London and would suspend the industrial action if the Major of London, Boris Johnson, suspended plans to close all ticket offices on the network.
Members of the RMT and the Transport Salaried Staffs Association are due to walk out for 48 hours from 9.30pm on (Tuesday) 4 February and again a week later job losses they say will follow the closures.
"More and more people want to use the underground and you're going to take around 800 jobs away to deal with those people," said Crow.
"[The ticket office supervisors] play a crucial role. They are visual, they've got experience, and when the [7/7] bombings took place by the vicious terrorists in London, these are the people who came from behind the back of the booking offices to support those group of passengers who were travelling around London to get them to a safe place."
His statement came amid reports that he recently enjoyed a £10,000 holiday.
In response to an accusation by a reporter that he was a distraction from the issue at the heart of the dispute, Crow denied that the unions' objectives was undermined by his high profile and stressed that his holiday was "booked up well before" the strike action.
"If I'm going to spend £10,000 on a car, or if I'm going to spend £10,000 on a holiday, or £10,000 on cigarettes, that's up to me," said Crow.
"I'm not being a distraction at all. What do you want me to do? Sit under a tree and read books of Karl Marx every day?"
Johnson has offered to hold talks between the two sides but only if the industrial action were called off. He accused Crow of trying to hold the capital to ransom.
Crow said: "Our message to the mayor is quite clear. We are prepared to suspend the industrial action, if [Johnson is] prepared to suspend the job losses."
But Johnson wrote, in a column for the Daily Telegraph: "What [Crow] should certainly not be able to do is prepare to disrupt the lives of millions of people who are not on holiday but who want to work, indeed, who need to get to work to earn the bread for themselves and their families – the bread that will allow them to pay for a holiday of a kind that Bob has been enjoying."
Transport for London and the trade unions are in negotiations at the conciliation service Acas.
"Our customers and staff are at the very centre of our plans for London Underground," said Mike Brown, London Underground managing director.
"All Tube stations will remain staffed and controlled at all times when services are operating, and we'll be introducing a 24-hour service at weekends during 2015.
"In future, there will be more staff in ticket halls and on platforms to help customers buy the right ticket, plan their journeys and to keep them safe and secure.
"We're committed to implement these changes without compulsory redundancies and there'll be a job for everyone at LU who wants to work for us and be flexible."