The biggest union for Tube workers will meet on Friday to discuss their next move after holding security talks with London Underground (LU) on Wednesday.
LU wants to increase police patrols on the Tube
The Rail Maritime and Transport (RMT) union said it may ballot for industrial action if its demands are not met.
It is calling for more rail guards on trains and better emergency training and equipment, including breathing apparatus for rail staff.
LU said more police patrols is the best way to increase security on the Tube.
The RMT's general secretary Bob Crow said: "We were concerned to hear suggestions that funding for improved security would have to depend solely on passenger revenue, especially as we were told that revenue was 'heading south' after the recent bombing attacks.
Risk not fear
"I am sure that the travelling public would join with our members in insisting measures to improve security on the capital's transport network should not have to rely on passenger revenue."
Howard Collins, LU's service director, said it was the sixth "constructive meeting" with the unions since the attacks of 7 July.
He added: "Any changes should be based on risk not fear.
"As the mayor has stated we believe the best way to increase security on the Tube is to continue to increase the number of police on the network who are properly trained to deal with terrorists and are mobile, rather than to have a guard who is stuck at the back of a train.
"There is currently a record number of British Transport Police officers patrolling the network in addition to the Met Police."
The RMT's executive will meet on Friday to discuss security on the underground.