Governors have threatened to take administrative and legal action against striking nurses who will not resume duty.
According to them, nurses should return to work because they are taking part in an "unprotected strike".
In a letter addressed to the Kenya National Union of Nurses officials, the county leaders say that the association did not adhere to the recognition agreement, the KNUN constitution and the labour relations law when it called for the industrial action.
"Knun must demonstrate proof of compliance with the recognition agreement and its constitution within 24 hours failing which, as employers, county governments will take "appropriate" administrative and legal action," a letter signed by Kisii Governor James Ongwae, who is the chairman of the Council of Governors' Human Resources, Labour and Social Welfare Committee, says.
In the document seen by the Nation, the governors says that it is unjustified that the current strike is a continuation of the 2016 industrial action since the return-to-work formula signed last year ended that strike.
If the union is dissatisfied with the negotiation process, governors say, it should have lodged a dispute with the Labour Cabinet Secretary.
"A return-to-work formula serves as an end to industrial action and any new strike must go through the process provided for under the Labour Relations Act," the letter says.
But nurses have vowed to stay put, arguing that the boycott was justified since the grievances raised in last year's strike had not been addressed.
"We are in receipt of the governors' letter and have responded. However, I must say that, as long as our grievances are not addressed, we will not go back to work," KNUN acting chair Joseph Ngwasi said.
Meanwhile, KNUN's branch in Nandi has called off the strike for its 500 members in 194 health facilities and advised to report back to work, saying the industrial action was illegally sanctioned by secretary-general Seth Panyako.
"We are advising our members to resume duties latest Friday morning because we have read a sinister motive behind the strike," the union's secretary in the region Amos Ng'etich said. He warned that members who defy the directive will face disciplinary action.