The Council of Governors has maintained that county bosses will sack all nurses who have not resumed duty and advertise their positions.
The CoG has described the nurses' strike as illegal and unprotected.
In a statement issued Sunday, CoG chairman Josphat Nanok said the Employment and Labour Relations Court, on September 1, declared the nurses' strike illegal.
He asked officials of the Kenya National Union of Nurses (Knun) to call off the strike immediately and refrain from interfering with the smooth running of health care in Kenya.
The statement was issued following a CoG consultative meeting held in Nairobi on Friday to discuss strikes by the nurses and clinical officers.
Those who attended include Health Cabinet Secretary Cleopa Mailu and Principal Secretary Julius Korir; Public Service Commission chairperson Margaret Kobia; Salaries and Remuneration Commission chairperson Sarah Serem and SRC chief executive Anne Gitau; and County Public Service Boards Human Resources Committee chairman Eliud Mureithi.
"Our consultative meeting reiterated the resolution of the council meeting of August 31, 2017, that all nurses who have not returned to work stand sacked and thereafter, the counties advertise their positions," said Mr Nanok.
He added that the nurses do not have recognised agreements with the 47 county governments and their strike is, therefore, illegal.
He further said county governments are the only ones mandated to deal with their employees and resolve any dispute.
He said the duty of the SRC is to manage civil servants' expectations by making public job evaluation and grading reports for all cadres of civil servants, including those in the health sector, and the grading tool used.
The nurses have been boycotting work for over three months, demanding the implementation of their Collective Bargaining Agreement (CBA).
At the same time, Knun has faulted the governors' council for insisting that it will not coordinate the joint signing of the CBA, describing the move as "malicious and blackmail".
In a statement, Knun secretary-general Seth Panyako said the council was violating a law that requires it to perform the coordination role.
He called for the council's abolition, saying it had failed to discharge the core mandate for which it was established.
Mr Panyako said Justice Nduma Nderi, in his judgment on petition No. 70 of 2014, expressed the need for a joint negotiation mechanism with the council for all the health employees to have a common CBA across all the counties.
"Nonetheless, the union has no problem negotiating with the individual county governments to reach a solution to the issues affecting the nurses, including signing of individual CBAs," he said.
The secretary-general dismissed the constant pronouncements by politicians and some governors that the strike is illegal.
He said judge Nderi "pointed out that workers in Kenya have a right to go on strike as provided under article 41(2) (d) of the Constitution and so we call upon nurses to remain calm and not to be tempted to deviate from a war they are about to win".
He criticised the final job evaluation report released by the SRC on September 18, saying it was misguided.
"We wish to denounce and totally reject the report, which continues to grade nurses in the band of unskilled employees and say we are no longer bothered with the contents as we will pursue a lasting answer elsewhere very soon," he said.