Health union leaders have urged Rishi Sunak to resolve the deepening NHS pay dispute in the next two weeks to stop the biggest strike in the service’s history going ahead on 6 February.

They made their plea as about 16,000 paramedics, call handlers and other ambulance staff in England held the latest stoppage on Monday in their campaign against ministers’ imposition of a below-inflation £1,400 pay rise.

Sharon Graham, the general secretary of Unite, said 6 February, when nurses and ambulance personnel are to stage unprecedented joint strike action, was set to be “a very bad day for the NHS”. However, the prime minister could avoid that by making unions a fresh offer on salary levels for 2022/23 that they could then ask their members to vote on, she said.

The planned strike makes 6 February “an important day but it’s a day that I hope does not happen,” she said. “There’s many, many days between now and 6 February and I hope what the government do is come to their senses, get the general secretaries around the table – we will be there any time, any place, anywhere – and do this deal.”

Speaking to LBC, Graham added: “So I really hope that 6 February doesn’t go ahead because the government puts an offer on the table. If they don’t do that of course it will go ahead [and] it will be a very bad day for the NHS, everybody will feel that. But we have no other alternative.”

She urged Sunak to use the next 13 days to engage in face-to-face talks because it was clear, she said, that Steve Barclay, the health secretary, does not have the authority to end the dispute.

Barclay is understood to agree with the unions’ central demand, that staff get more than £1,400 for 2022/23, and that new money is needed to fund any deal, rather than the health budget being raided for the several billion pounds NHS insiders believe would be needed to do a deal.

However, the situation has reached an impasse because Sunak and the chancellor, Jeremy Hunt, have made it clear they will not provide any new money to cover a bigger award.

And in remarks that confirmed the deadlock between unions and ministers, Sunak made clear on Monday that he could not “wave a magic wand” to end the public sector pay war.

He told ITV: “Taking a step back, of course, it would be lovely to be able to wave a magic wand and just give everyone what they were demanding when it came to pay.”