The company has been in dispute for more than a year with the RMT over changes to guards' roles on trains.
RMT conductors saw the changes as a ploy to phase out a second person on trains. It has now proposed a six-month trial with two staff guaranteed on all affected services.
But Southern said what the RMT wanted was "a guarantee to cancel trains".
Under the changes to guards' roles, which were also opposed by the Aslef train drivers' union, responsibility for opening and closing doors passes to the driver rather than the conductor.
The practice is called driver-only-operation (DOO).
Southern rail strike: What's it about?
RMT leaders have set out an "accessibility guarantee" plan, which would ensure a driver and an on-board supervisor staff all trains.
This would mean disabled, elderly and vulnerable passengers would be provided with guaranteed assistance from on-board staff on all services without the need to book in advance, the union said.
RMT general secretary Mick Cash said: "We are hoping the company will reconsider our proposal for a trial six-month period of an accessibility guarantee.
"We would hope that they would agree to this sensible proposal as the Association of Train Operating Companies consultant's report has said train companies should guarantee a second person to comply with their legal obligations."
But a spokesman for Southern said: "The guarantee the RMT wants is a guarantee to cancel trains. We want to put the passenger first and keep trains running.
"Driver-controlled operation is safe and provision for those who need assistance has not deteriorated while, at the same time, service levels have steadily improved."
RMT members on Southern will stage a fresh strike next Monday, while Aslef has banned overtime.

An army spokesman said a total of 253 people had been summoned. Fifty-three did not report and 76 were in custody.
Conditions for the release appear to include agreeing to avoid political activity and informing the army of travel, a BBC correspondent says.
Coup leaders, who took power last week, received royal endorsement on Monday.
Thailand's former prime minister, Yingluck Shinawatra, has been released but remains under some restrictions.
The army also says it is releasing a group of "red-shirt" protest leaders who support the ousted government. The anti-government protest leader has already been freed.
So far, almost all of the 124 people who the army said they had detained and released have kept a very low profile, says the BBC's Jonah Fisher in Bangkok.
It remains to be seen whether these "red-shirt" leaders - who support the ousted government - do the same, our correspondent adds.
The military seized power in Thailand on 22 May, saying it wanted to return stability after months of unrest.
The move followed six months of political deadlock as protesters rallied against Ms Yingluck's government.
At least 28 people were killed and hundreds injured during the protests.
On Monday a royal command approved the coup. But the military's actions in removing an elected government has drawn widespread international criticism.
Correspondents say there is also a degree of scepticism about the total number of people in custody provided by the military, with reports of more widespread detentions.
Rights groups have expressed alarm over the detentions, as well as the tight restrictions on media.
On Monday, there were reports that internet users were briefly unable to access social media site Facebook. The country's information and technology ministry told the BBC there was a gateway problem.
Experts have said that the coup is unlikely to heal highly polarised political divisions in the country.
The current deadlock dates from 2006, when the military ousted Ms Yingluck's brother, Thaksin Shinawatra, in a coup.
Both have strong support in rural and northern areas, propelling them to successive election wins.
However, many in the middle class and urban elite, who comprise the heart of the anti-government movement that began in November 2013, oppose them bitterly.
Union leaders have held talks with MPs over a plan they claim could end the long-running row on Southern rail.
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Thailand's army says it has now released 124 people, including politicians and activists, who were taken into custody after the coup.