The union says ministers must respond within 48 hours of next week’s walkout to avoid more action.
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The government has reiterated it is “resolute” on pay after nursing unions threatened to escalate strike action if ministers do not engage in talks within 48 hours of Tuesday’s walkout.
Members of the Royal College of Nursing (RCN) are due to stage a second strike on 20 December.
Cabinet minister Oliver Dowden insisted ministers were “reasonable” but had a duty to keep finances under control.
The government said an independent pay review body decided pay for nurses.
The RCN is calling for a pay rise of 19%, but union leader Pat Cullen said this was a “starting point” and any new offer would be put to members.
The NHS Pay Review Body recommended a £1,400 raise, with slightly more for experienced nurses – an increase of about 4% on average, although the government says it represents at 9% rise for those on a starting salary.
Urging the unions to call off the strike, Mr Dowden told the BBC’s Sunday With Laura Kuenssberg: “We will be resolute to this, because it would be irresponsible to allow public sector pay and inflation to get out of control and we owe a wider duty to the public to make sure we keep our public finances under control.”
Challenged about its reluctance to engage on pay, the Cabinet minister in charge of contingency planning for strikes, said the government was “always willing talk”.
“We’re trying to be reasonable, we’re trying to be proportionate and we’re trying to be fair,” he said.
The RCN’s strike on Thursday was the largest in its history. Across England around 9,999 staff were absent, while nearly 16,000 appointments, procedures and surgeries were rescheduled.
It involved around a quarter of hospitals and community teams in England, all trusts in Northern Ireland and all but one health board in Wales. Nurses are not striking in Scotland.
Ms Cullen said an escalation would involve a greater number of hospitals and scaling back support for non-emergency services.
During action so far the RCN has said it will still staff chemotherapy, emergency cancer services, dialysis, critical care units, neonatal and paediatric intensive care.
Some areas of mental health and learning disability and autism services are also exempt.
The action by nurses will be followed on 21 December by a strike by ambulance staff, who will also take industrial action on 28 December.
The co-ordinated walkout was called by the three main ambulance unions – Unison, GMB and Unite.
All three are taking action on 21 December. GMB union members will go on strike again on 28 December.
Around 1,200 members of the military are being drafted in to cover for both ambulance staff.
However, unions warn military staff are not “sufficiently trained” .
Sara Gorton, head of health at Unison, said there was “unfortunately more risk” to patients during a strike, but said: “Every single day patients are being put at risk because of the staffing crisis”.
Unison says there are 133,000 vacancies across the health service.
Industrial action has also been taken by rail workers, Royal Mail staff and other sectors in recent weeks over pay disputes as the cost of living rises.
The government has announced it will publish a new “resilience framework” on Monday, aimed at improving how the UK prepares for and responds to critical issues like strikes.
The framework will “bring together all levels of government, critical national infrastructure operators, the private sector, charities and the public to bolster our national preparedness to these risks”, the Cabinet Office said.
