Railway staff outside stand on the picket line during a rail strike in a long-running dispute over jobs and pensions, outside Ashford International station in Kent, Friday, Jan. 6, 2023. AP
Each government department has written to union leaders representing striking workers in its area of responsibility, to invite them to meetings on Monday, he told reporters.
"We incredibly value the important work that our public-sector workers do, especially our nurses, and we want to have an honest, grown-up conversation about what's affordable, what's responsible for the country," Sunak said.
"Those invitations have gone out and I'm hopeful that those meetings can happen on Monday so we can have a productive conversation and find a way through this."
The invitation represents a volte-face of sorts after the government had long insisted that it could not negotiate directly with nurses or railway staff, only via their direct employers.
Train drivers were on strike again Friday, forcing many Britons to work from home, and the union for junior doctors said it was holding a ballot to join nurses in their own unprecedented walkout.
The strikes mainly revolve around pay, which has failed to keep up with eye-watering inflation that breached 11 percent in October.
Among others striking this winter have been ambulance workers, border security personnel, and postal delivery staff.
The government responded Thursday with a vow to enact new legislation requiring a minimum level of key public services during strike action, on pain of legal action against union leaders.
Sunak said he "fully" supported workers' right to strike.
But the legislation would bring Britain into line with others such as France, Italy, and Spain "so that even when strikes are going on you know that your health will be protected", he said.
"I think that's entirely reasonable and that's what our new laws will do."