As nurses in public hospitals insist on boycotting work, a court granted governors their wish and suspended the ongoing strike for 60 days.
Council of Governors chairman Wycliffe Oparanya said the court ordered nurses and their employers to attend conciliation meetings initiated by Labour and Social Protection Cabinet Secretary Ukur Yattani.
Last week, Mr Yattani formed a committee to look into issues raised by nurses and file a report within 30 days.
The governors' council moved to court to challenge the legitimacy of the strike.
The health workers and devolved governments are required to file reports in court and wait further directions.
Kenya National Union of Nurses Secretary-General Seth Panyako dismissed calls for a meeting.
"We shall only engage in negotiations if the agenda is grading structures and harmonising salaries," he said.
The union accused the Labour Ministry of frustrating the implementation of the agreement reached by nurses and county governments.
Mr Panyako said devolved units "are playing with the nurses minds by failing to honour the agreement the parties in dispute signed on November 2, 2017".
The nurse are demanding uniform and nursing service allowances.
Nurses earn Sh20,000 every month in service allowance, which was to be increased to Sh30,000 over three years from 2017. The uniform allowance was raised to Sh10,000.
On Monday, nurses in West Pokot, Kisumu, Nairobi, Kisii, Taita-Taveta, Nyandarua, Trans Nzoia, Elgeyo-Marakwet, Wajir, Nyeri and Kitui counties went on strike.
Nurses in Homa Bay and Marsabit counties had planned to go on strike this morning while those in Kwale, Garissa, Samburu, Kirinyaga and Embu are to start theirs on February 11.
Those in Murang'a, Busia, Nakuru, Siaya, Narok, Makueni, Bomet and Tana River planned to go on strike from February 18.
The union has not called a strike in 18 counties, which have agreed to implement the return-to-work agreement.
Hospitals in Kisumu and Kisii counties were deserted Tuesday.
Patients at Mbagathi District Hospital in Nairobi were transferred to Kenyatta National Hospital and the rest handled by clinical officers and doctors.
Pumwani Maternity Hospital was offering services, more than 30 hours after the strike began.
Pumwani Hospital administrator Geoffrey Mosiria said nurses there are not members of Knun but belong to the County Government Workers Union.
"The workload may increase. Seventy-six nurses are on duty in three shifts daily. The hospital handles 220 admissions a day," he said.
Public dispensaries in Kayole remained operational.
Reporting by Angela Oketch, Aggrey Omboki, Verah Okeyo and Collins Omulo