London Underground Ltd (LUL) has made what it claims is a final offer in an attempt to end a pay and jobs row which led to a 48-hour strike last month.
The two-year deal would see a 1.5% rise in the first year followed by RPI plus 0.5% the next year. LU's offer did not assure jobs, a main demand of a union. The RMT said it hoped to make "positive progress" on the issue of no job cuts.
The union went on strike as LUL failed to meet its promise of no compulsory redundancies as well as those on pay and management bullying.
The new pay offer is an improvement of 0.5% in the first year for the 25,000 staff.
LUL's interim managing director Richard Parry said: "This is a very fair offer made in tough economic times.
"We would now expect all unions to accept this final offer and recommend it to their memberships."
Bob Crow, the RMT general secretary, said: "The offer is under consideration and RMT is looking to make positive progress in the crucial, on-going talks on job security."
The management is still in talks with the RMT over compulsory redundancies. LUL has claimed that it wants to avoid compulsory lay-offs, but warned ominously that some jobs would have to be cut.
Nine tube lines were affected by the 48-hour industrial action as commuters struggled to get in to work on crowded buses and gridlocked roads. Many were unable to attend work entirely costing London's economy millions of pounds. Though many in the media have attempted to claim the strike was broken, the facts speak for themselves. On a normal day 522 trains are run across the combine. Taken as a percentage, and at mid peak times (0900 and 1800) the best 'service' LUL were able to run amounted to 28% on Thursday (0900).
However, without the Northern and Jubilee Lines the best 'service' they could run across the combine was 17% for Wednesday and 19% for Thursday.