The deal does not fulfil their demands regarding the matter of internship postings for medical graduates.
Kenya is grappling with a significant healthcare crisis as workers continue to strike, demanding better working conditions.
CS Nakhumicha urges the KMPDU "to do the honourable thing and call off the strike that has, on several occasions, been declared illegal."
The Kenya Medical Practitioners Pharmacists and Dentists Union (KMPDU) underscored the enduring grievances against the government, which are yet to be resolved.
The healthcare system has long been overburdened and underfunded, but it has ground to a near halt after about 7,000 professionals walked off the job.
KMPDU Secretary-General Davji Atellah told the press that they must fight for interns, as they are the most vulnerable group in the profession.
Government officials say they are heading to court to seek clearance to have all the medics fired and replaced.
The government is seeking 30 more days for the negotiations, a period during which it wants doctors to provide minimum services.
They have also vowed to take legal action against the striking medics for absconding duty.
The rights body is pushing for talks to end the strike and wants the immediate end of threats by the government.
They say they delayed their strike to keep from burdening the people during Ramadan.
KMPDU say they follow proper channels to ensure peaceful demonstrations but are met with threats of force and intimidation.
Police IG Koome said medics participating in the strike have become a public nuisance, using whistles and vuvuzelas during demonstrations.
Desperate for medical attention amid the doctors' strike, some say they have no choice but to turn to pharmacists, who may be unqualified.
CS says striking doctors have attempted to intimidate and threaten violence against health workers who have opted out of the "unlawful" industrial action.
Like other cancer patients across the country, Florence is afraid that delayed treatment could dim her chances of successful treatment.
The doctors have accused the county leadership of lacking goodwill in solving their issues.
Led by party leader Raila Odinga, they accuse the government of responding inadequately to a serious crisis.
The medics condemned recent threats issued by various county governors, management of national referral hospitals and Ministry of Health demanding doctors to return to work under duress.
The medics are now calling for a meeting with President William Ruto as they seek a resolution to end the stalemate.