Transport chiefs have launched a fresh attempt to avoid RMT industrial action on the London Underground next week.
The RMT union is planning two 24-hour walkouts by Underground drivers on Tuesday June 2 and Thursday June 4.
Tube services could also be hit the day after the strikes due to the knock-on effect.
Transport for London (TfL) and RMT officials held talks on Tuesday to try to resolve the dispute which is over a four-day week for Tube drivers.
TfL has previously stressed that the proposed four-day week would be voluntary and no driver would be forced to accept it.
It is giving further assurances that the voluntary nature of the offer would remain in place and it would not become compulsory if a small number of drivers declined to accept it.
The RMT is understood to have asked for clarification on a number of other issues.
The union’s representatives were believed to be meeting on Wednesday, which could influence whether the strikes go ahead next week.
Two 24-hour walkouts earlier this month were called off amid growing questions over the level of support within the RMT for the industrial action.
The RMT’s position on the strikes was weakened after the Aslef train drivers’ union firmly backed the four-day week offer.
TfL is not expected to change details of the deal.
But it could give more clarification to the RMT over aspects of the proposed new working conditions.
Such reassurances could pave the way for the union to decide to recommend to its members to accept the reforms.
Alternatively, the RMT could press ahead with more industrial action.
But the effectiveness of its strike action in April was cast into doubt by more than 50% of services running on the Underground.
Some RMT drivers turned up to work.
The RMT has branded the TfL proposals as a “fake” four-day week, arguing it was compressing five days of work into four.
It has also raised concerns that the changes could lead to more fatigue among drivers and that they might only be told their shifts at short notice.
But Aslef hailed the deal on offer as the “biggest improvement in working conditions for Underground train drivers in decades”.
It stressed that Tube drivers would get “working conditions that are as good as, or better than, those on any mainline train company”.
Benefits highlighted by the union to its members included an extra 35 days away from work a year, and average weekly rostered hours being cut to 34 from current average of 36.
It also emphasised that the changes would make it easier to arrange roster patterns to block leave together, or take long weekends or mini-breaks, and would save money on travel and childcare costs.
For the first time, drivers would be allowed to volunteer for overtime which would be paid at time and a quarter.
London Mayor Sir Sadiq Khan has urged TfL and the RMT to get around the table to thrash out as solution to avoid more disruption on the Tube network.
Meanwhile, more than 300 bus drivers at Bow bus garage, east London, were striking for three days from Wednesday May 27, with more walkouts planned from June 11 to 14, in a row over rotas and driver fatigue.
