The crisis in public hospitals is likely to worsen as some county governments gave the striking nurses a week to return to work or face the sack.
However, the nurses dug in saying they will not return to work without the Council of Governors signing the Collective Bargaining Agreement that improves their terms.
Private hospitals across the country are congested with an increasing number of patients seeking treatment.
Some public hospitals said they were running out of essential drugs as the nurses' strike enters its fourth month to demand better pay, allowances and working conditions.
Elgeyo-Marakwet Governor Alex Tolgos threatened to sack all striking health workers and advertise their jobs by next Monday.
"We are giving all the striking nurses up to Friday this week to get back to work," Mr Tolgos said.
In West Pokot, Governor John Lonyangapuo is set to meet the striking nurses on Tuesday in a bid to resolve the stalemate.
He cautioned politicians against inciting the workers not to resume duty.
"We are ready to hold talks with nurses. We don't want our people to continue suffering," he said.
Turkana Health executive Jane Adele said most health facilities in far-flung areas had received 90 newly employed nurses and health services are still ongoing.
In Bungoma, Kenya National Union of Nurses branch secretary George Shibeka said he was hopeful the union's talks with the governors will resolve the stalemate.
"The strike is still on and currently the union and Council of Governors are meeting under the Labour ministry to try and end the strike," he said.
In Nandi, services are back to normal after Governor Stephen Sang brokered a deal with the nurses last week that saw them return to work.
In Nyeri, the union threatened to fine nurses who had gone back to work without the deal being signed.
According to branch secretary Beatrice Nduati, each nurse who had resume duty would be fined 2.5 percent of their monthly salary for the next four years.
Expectant mothers and newborns are the most affected by the strike.
A spot check in various public health facilities in Nakuru County, including the Nakuru Level Five Hospital and Molo sub-county hospital, revealed that a huge percentage of expectant mothers had been forced to pay up to Sh15,000 to get maternity services in private hospitals.
"Private facilities are too expensive for us. It has forced some of us to opt for home deliveries, which are not safe," Ms Eunice Njoroge, a mother, told the Nation.
In Narok, there were no admissions in most hospitals with patients being discharged to enable them seek services in private hospitals.
On Monday, only doctors were seen attending to patients and those who needed the services of nurses and clinical officers were turned away.
In Busia, nurses appealed to Governor Sospeter Ojaamong to prevail upon his colleagues to sign the CBA, saying they were ready to work.
However, Busia County Health Chief Officer Asoka Itur threatened to stop the nurses' September salary if they failed to report to work.
The situation was the same in Homa Bay, where nurses claimed governors were deliberately delaying the signing of the CBA.
In Kisii County, acting Health services chief executive Raymond Oigara said they were still awaiting communication from the county secretary before they write warning letters to the striking nurses.
"We will begin writing show-cause letters as soon as we get communication from the employing agency," he said.
Some patients in Mombasa, Kwale and Taita-Taveta counties are now seeking treatment in Tanzania due to the health crisis.
Patients are also flocking to medical camps organised by charity organisations.
On Sunday, more than 1,500 people were treated during the Mabati Rolling Mills free medical camp at their Mabati Medical Centre in Kilifi.