The RMT has called for urgent talks ahead of a meeting to discuss further strikes on the Southern rail network.
Southern has called on the conductors' union to end its action and said the strikes are increasingly "ineffective".
The operator said it ran nearly 90% of trains during a one-day walkout by the RMT this week.
Meanwhile, Aslef met Southern on Wednesday in a bid to avert further strikes by the drivers' union after its members rejected a deal.
Aslef has said it is working to ensure there are no more drivers' walkouts, but it still has a mandate to strike. Southern is unable to run the majority of its services during train driver strikes.
The BBC understands those discussions will also resume next week.
Both unions have been in dispute over driver-only operated (DOO) trains.
The row is over Southern's decision to turn guards into on-board supervisors and give responsibility for opening and closing carriage doors to drivers.
RMT chief Mick Cash said the union had written to parent firm Govia Thameslink to stress the urgency of talks ahead of a union meeting on Tuesday, and to seek assurances on safety.
He said: "RMT continues to seek a guarantee on a second safety-critical member of staff."
A Southern spokesman said the company was reviewing the letter but said: "We ran nearly nine in 10 train services during the RMT strike two days ago and over half (54%) of our on-board supervisors and conductor staff reported for work on the day too."
"The RMT leadership should recognise these facts and that our passengers are noticing that the RMT's action against them is increasingly impotent and ineffective."
An RMT member said it was a "pack of lies from a company which wouldn't know the truth if it hit them in the eye".