The threat of a Tube strike has been averted after the mayor gave assurances over security fears in the wake of the London bombings.
RMT members will not be balloted on industrial action
Rail Maritime and Transport (RMT) union leaders said progress was made over safety equipment and staffing levels during talks with Ken Livingstone.
RMT general secretary Bob Crow said they would not be balloting members.
London Underground (LU) pledged to work constructively with the unions on the issues of security and safety.
Mike Brown, LU chief operating officer, said: "Our staff continue to work professionally to keep London moving.
More visible staff
"Obviously we are committed to working with all the trades unions constructively on the challenges we face on security and safety, as always guided by the advice of the British Transport Police."
Mayor Ken Livingstone said: "There has never been a proposal to reduce the level of staffing on the Tube.
"London Underground management will be looking at ways to improve safety and security and to reassure passengers in the weeks and months to come.
"One important step in this direction will be to start to deploy more visible staff in public areas."
Mr Crow said they would be seeking talks with rail firms to discuss security and safety issues.
He said there remained a disagreement over its call for rail guards to be reinstated on Tube trains after the attacks in London.
Rail guards were last in operation in 1999 on the Northern Line and were phased out with the introduction of CCTV on trains which allowed drivers to see the platform.
Following Friday's meeting, Mr Crow said the mayor had made a commitment not to reduce staffing and agreed that any train without a working communications radio would be taken out of service.
He added there would be further discussions on matters such as better emergency training and equipment, including breathing apparatus for rail staff and the strengthening of drivers' cabs.