On the eve of the biggest week of strikes in NHS history, Unite's Sharon Graham said: "Where is Rishi Sunak, why is he not at the negotiating table?"
It came after the head of a nurses' union urged the PM to offer a new deal to avert nursing strikes in England.
The government insists its £1,400 rise for NHS workers this year is fair.
But Unite and other health unions say the increase - an average rise of 4.8% - fails to reflect rising living costs, and needs to be increased.
Health Secretary Stephen Barclay says he has held "constructive" talks with unions over pay for the next financial year, starting in April.
But speaking on BBC One's Sunday With Laura Kuenssberg, Ms Graham said Unite "are in no talks at any level whatsoever" with the government about NHS pay, accusing ministers of an "abdication of responsibility".
Calling on the prime minister to get personally involved in finding a solution, she said: "Instead of doing sort of press conferences about other things, come to the table and negotiate - roll your sleeves up and negotiate on the pay in the NHS."
Her call for Mr Sunak to intervene in the dispute over NHS pay in England follows a similar appeal from Pat Cullen, general secretary of the Royal College of Nursing.
In a letter to the prime minister on Saturday, Ms Cullen wrote: "I am appealing directly to you for the first time: address this current impasse."
The RCN and several other health unions in Wales have suspended planned action next week after the Labour-run Welsh government offered NHS workers an extra 3% on top of the £1,400 for this year.
The RCN, along with the GMB union and the Royal College of Midwives (RCM), has also put strike action on hold in Scotland to allow further talks on the 2023 pay offer.
In her letter, Ms Cullen said the UK government was looking "increasingly isolated" by "refusing to reopen" talks over this year's pay deal in England.
Ambulance workers represented by Unite are still set to strike in Wales next week, after the union decided against joining others in suspending action.
But Ms Graham told Laura Kuenssberg she would be meeting with the Welsh health minister later, in a bid to find a deal.
She added that the Welsh government needed to "come back to the table" with an improved offer - but added the situation in Wales and Scotland was in "stark contrast" to the impasse in England.
Speaking on the same programme, Business Secretary Grant Shapps defended the government's approach to pay in England, adding that the £1,400 rise had been suggested by the NHS pay review body.
The government says it wants the body, made up of eight advisers, to recommend a pay award for next year in April.
However, the health department is yet to present its submission to the body - a key step in the process of drawing up a recommendation. The review body says it has evidence from the Treasury.
Health unions have said they won't formally submit evidence until the dispute over this year's pay is resolved, instead publishing a document setting out their argument for higher pay.
Monday will see combined industrial action in England, as members from the Royal College of Nursing will walk out alongside call handlers, paramedics and other ambulance staff - who are members of either the GMB and Unite unions.
The strike will affect non-life threatening calls only and people are advised to use the 999 service in an emergency.
Tuesday will see members of the RCN union go on strike again. The union represents roughly two-thirds of NHS nurses.
They are taking industrial action over pay, but life-preserving treatment must be provided, and all nurses in intensive and emergency care are expected to work.
NHS physiotherapists across England will go on strike on Thursday over pay and staffing, and the Chartered Society of Physiotherapy (CSP) says 4,200 members are involved.
And on Friday, thousands of ambulance staff across five services in England - London, Yorkshire, South West, North East, and North West - are striking.
We are not in talks with government over pay - Unite boss