President Uhuru Kenyatta has ordered all nurses to report to work by February 15 or face dismissal by the county government and the Health ministry.
Last week, the court suspended the nurses' strike for 60 days.
This was after the Council of Governors sought an injunction to enable both parties to negotiate.
But some nurses have refused to honour the directive from the courts saying they have to be heard by their employer.
"Any nurse who fails to report to work will be dismissed by the county and the ministry of health. The government will be at liberty to take any action as they deem appropriate," Uhuru said.
Speaking when he addressed the nation on Wednesday after meeting the Council of Governors, Uhuru said Kenya has a clear development agenda and they cannot allow unlawful industrial action to derail Kenyans from taking the country forward.
"As the Commander-in-Chief, I have instructed the National Police Service to take stern action against picketers who might harass public service for going to work," he said.
Uhuru said it is disheartening to learn that some nurses have decided to engage in an unlawful withdrawal of their labour to Kenyans against the determination of the court which suspended any industrial action.
"It is disheartening to hear officials of the nursing union declare that they will not obey court orders.
One of the most important principles our republic has established is the rule of law and no one is above the law," he said.
"Obeying court orders is not optional and it is a requirement of all of us no matter their place in the society."
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After the address, the National Nurses Association of Kenya national chair Alfred Obuya said the directive by the president is likely to change the course of things.
"It is a directive that is likely to change the course of things but it is a bitter pill we have swallow," he told the Star on phone.
CoG chairman Wycliffe Oparanya on Tuesday moved to court to challenge the legitimacy of the strike by the Kenya National Union of Nurses.
Nurses in 23 counties went on strike on January 4 demanding the implementation of the 2017 return-to-work formula.
KNUN secretary general Seth Panyako said only Machakos, Mombasa and Migori counties have fully implemented the October 2017 CBA.