After years of underfinancing, the NHS state-funded health service is struggling to meet the demand for emergency medical care during a particularly difficult winter with high rates of coronavirus and flu.
Hospital and ambulance staff have launched rare strike action -- in the case of the nurses, for the first time in 100 years -- with many members of the public sympathetic to their cause.
Nurses are calling for a salary hike to reflect inflation soaring above 10 percent.
After being accused of inaction, Sunak was hosting England's chief medical officer Chris Witty, and NHS England chief executive Amanda Pritchard at Downing Street on Saturday.
The meeting came ahead of talks planned between government officials and union leaders on Monday, aimed at ending the strikes.
"During the pandemic we had to bring boldness and radicalism to how we did things in order to get through," the prime minister was quoted as saying by Downing Street.
"I think we need that same bold and radical approach now."
He added: "Together today, we can figure out the things that will make the biggest difference to the country and everyone's family, in the short and medium term."
In a speech this week Sunak set out five priorities for 2023 including shortening NHS waiting lists.
The general secretary of the Royal College of Nursing union, Pat Cullen, told BBC radio that she would attend the Monday talks with the health minister Steve Barclay.
At the same time she said that Sunak should negotiate with nurses directly to prevent planned further strike action on January 18 and 19.
"He needs to come to the negotiation table with me and he needs to put money on that table, and it needs to be about the current year," she told the BBC.
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