After five days of Tube strikes in September caused significant disruption to Londoners, the RMT said it wanted “steps towards” a reduction of three hours to a 32-hour week.
RMT general secretary Eddie Dempsey said the new offer “will now be discussed by the national executive committee and in consultation with the membership”.
He added: “The union remains in dispute with London Underground subject to the will of the membership under our democratic structures.”
Transport for London (TfL) has said that even a 30-minute reduction in the working week would cost £30m a year.
A reduction to 32 hours, according to TfL, would cost over £200m which it would then not be able to invest in the system.
For another strike to happen, union members would have to agree via an organised vote – known as a ballot.
If workers agree to strike, details must be given to TfL at least 14 days before industrial action begins, unless the union and employer agree to seven days.
The RMT has said fatigue and extreme shift rotations are serious issues affecting its members’ health and well-being.