The firm's parent company, GTR, has said an offer, which includes a Â£2,000 bonus, "cannot be available indefinitely" if strikes continue.
But RMT bosses said the union had already rejected the offer, and accused Southern of using "threats and bullying".
A two-day strike is scheduled to begin on Friday.
The latest twist in the dispute comes as Southern reinstated a full timetable after three months of reduced services.
An increasingly bitter dispute has caused months of disruption for passengers, as RMT members staged a series of strikes in protest at GTR's plans to change the role of conductors on Southern services in South East England.
Rail chiefs made a "full and comprehensive offer" to the RMT on 3 October in an attempt to settle the impasse over the proposed operation of driver-only trains on the network.
But in a letter to RMT general secretary Mick Cash, GTR said: "Should your next planned action proceed... the offer is withdrawn in its entirety and will no longer be available for the RMT to accept."
Mr Cash said in a statement: "This is just more threats and bullying from Southern rail and does nothing at all to resolve the current safety dispute.
"It's also completely meaningless as the union has already rejected the Â£2,000 bribe to sell out safety, and the company are well aware of that."
At the height of the dispute, in July, Southern introduced a temporary timetable to help cope with staff absences, which compounded the problems caused by the strikes.
The standard service was reintroduced on Monday, although it got off to a difficult start due to a broken-down train at Crawley, while trains between Eastbourne and Hastings were hit by a signal problem.
A further three blocks of strikes are planned before Christmas.

The new world was found beyond our Solar System, 100 light-years away.
It's been named 51 Eridani b and is only 20 million years old - very young by astronomical standards.
The alien world could give us more information about the formation of our Solar System.
The find was made by the Gemini Planet Imager (GPI), which looks for young planets orbiting bright nearby stars.
Our own Jupiter is the largest planet in the solar system - it's so big you could fit over 1,300 Earths inside it!
It's also the fastest rotating planet too, with 1 day only lasting 10 hours - but a year on Jupiter lasts for 12 Earth years.
Jupiter doesn't have a solid surface and is made up of gas, giving it the name 'gas giant'.
The baby Jupiter has the strongest methane gas signature ever found on an alien planet.
The astronomers also detected water using the GPI's spectrometer instrument.
Scientists hope that by studying far away worlds, they can learn more about how common the structure of our Solar System is.
Astronomers believe the gas giants in our Solar System formed slowly - by building up a large core over a few million years and then pulling in a huge amount of hydrogen and other gases to form an atmosphere. This is known as a "cold-start".
But the Jupiter-like planets that have been discovered so far are much hotter than scientists have predicted. Which could mean they formed quickly - as gas collapses to make a scorching planet in what is known as a 'hot-start'.
Southern Rail's latest attempt to stop strikes on its network has been branded "meaningless" by union bosses.
[NEXT_CONCEPT]
Astronomers have discovered a baby planet which looks like a young version of Jupiter.