A 24-hour tube strike is due to go ahead after unions rejected a "new deal" from Transport for London (TfL).
But Sadiq Khan has instructed TfL "to continue negotiating".
Workers from the RMT and the Transport Salaried Staffs' Association (TSSA) unions are scheduled to walk out from 18:00 GMT.
The strike is expected to cause mass station closures.
Tube strike guide: What you need to know
The Labour mayor said TfL's negotiating team would "be available around the clock to resolve this dispute".
Calling the strike "pointless" Mr Khan said TfL's offer would "ensure station safety and staffing levels across the Tube network".
Steve Griffiths, chief operating officer for London Underground (LU), said the process had already begun to hire 200 extra station staff.
"Taking into account existing vacancies and natural turnover this means that over 600 staff will be recruited for stations this year."
The biggest rail union, the RMT, had walked out of talks at conciliation service Acas on Saturday.
On Sunday, the TSSA announced it had rejected the deal after consulting its members overnight.
TSSA general secretary Manuel Cortes said the new deal would not "restore Tube safety levels" with the "urgency that is now needed".
The offer was made after RMT left the meeting, a point the RMT disputes.
In a message to its members, RMT regional organiser John Leach said the talks had "failed" and the strike would go ahead.
Talks between both unions and London Underground (LU) had previously broken down on Friday afternoon.
No details of the latest deal were revealed but Mr Leach told members of the RMT that LU had "given exactly the same offer again" during Saturday's last-ditch talks.
"This is just not acceptable. The unsafe practices and pressure on staff and passengers have to be resisted and will be," he said.
Transport for London (TfL) previously said it would address the recommendations of a recent report, which found the closure of ticket offices had caused "significant issues" for Tube passengers.

Isabel Gentry, 16, was taken to Bristol Royal Infirmary after falling ill on 18 May and discharged four hours later.
Her mother Claire Booty said an initial assessment was "cursory and brief" and she "could hardly walk" when sent home.
In a review after the teenager's death, the NHS Foundation Trust said her treatment was "appropriate".
Isabel, who was known as Izzy, had been revising for exams when she started to feel unwell on 18 May. She was taken to hospital, by ambulance, at 01:00 GMT but was sent home at 05:00.
Ms Booty told the inquest, the hospital had said her daughter had a "viral infection of the stomach".
Avon Coroner's Court heard the teenager "could hardly walk to the car" when they left the hospital after the initial assessment.
Ms Booty said: "Izzy said 'Mum, I can't believe they're sending me home, I feel so ill'. She was not given a chance."
The court heard there had been a possible case of meningitis at her school, St Brendan's Sixth Form College in Bristol, a couple of weeks earlier and all students had been given leaflets explaining the symptoms.
Her mother said Izzy had the very symptoms described in the leaflet.
Paramedic Gary White, who was called out on 18 May, said he had been told the patient might have meningitis but said he "couldn't detect any major symptoms such as a rash or photophobia".
Ms Booty said her daughter "kept asking for the lights to be turned down" in the hospital treatment room.
She also said doctors "seemed to be distracted by another patient who was causing disruption at the emergency department".
The inquest heard that Izzy deteriorated over the day and another ambulance was called which took her back to the hospital at 17:30.
The consultant who treated Izzy diagnosed meningitis and told Ms Booty her daughter was "very seriously ill". Ms Booty told the court the doctor "couldn't believe she'd been sent home initially".
The next day an MRI scan detected Izzy's brain was swelling and she died, on 20 May, 48 hours after being initially discharged from Bristol Royal Infirmary.
The inquest is expected to last five days and will hear from paramedics, nurses and doctors from University Hospitals Bristol NHS Foundation Trust.
The Mayor of London has called for "last-ditch" talks to avert a strike on the London Underground hours before it is due to begin.
[NEXT_CONCEPT]
A girl who died of meningitis "was not given a chance" by the hospital which sent her home 48 hours before her death, an inquest has heard.