Taita Taveta residents seeking treatment at public health centres have reported difficulties getting drugs, with some being told to buy them from private pharmacies.
But Health department officials have denied the claims, saying they distribute medicines to all facilities.
Last year, officials set up a central drugs store in Wundanyi to track usage and curb theft.
A digital system was to be installed in the store to help monitor purchases of drugs and their usage.
Speaking when the store opened, Governor Granton Samboja raised the alarm over drug theft and wastage in health centres.
Hospitals are required to order drugs and other medical commodities and their pharmacists are supposed to replenish supplies immediately.
The governor, who had claimed unscrupulous health workers were involved in stealing drugs, said the store would help the county save millions of shillings being lost to theft.
A cartel was believed to sell the drugs to private pharmacies or stock them in private clinics.
Health executive John Mwakima dismissed claims of a shortage of essential drugs, saying the Wundanyi store was fully stocked and the department had distributed medicines to most health centres.
All health facilities in Taveta, Mwatate and Voi, he said, were well stocked with drugs and distribution was still underway in Wundanyi sub-county.
"As of now, all facilities have drugs. Distribution of drugs is a continuous process and we are on top of this," he said.
"We are guided by the (Kenya Essential Medicines List guidelines) and statistics from the health records and information office. Some of the medicines that patients buy in chemists are not in the category of essential drugs," he said.
Mr Mwakima said Taita Taveta has a good relationship with the Kenya Medical Supplies Authority (Kemsa), which distributes drugs.
The county, he said, has a debt of Sh46 million that he said will be settled once money becomes available.
"Sometimes the debt increases and sometimes it reduces. We don't have any problems with Kemsa because they have supplied us with drugs whenever we place our orders," he said.
He urged residents to avoid politicising health matters in the county.
"Our primary goal is to ensure that patients get services. We have the interest of residents at heart," he said.
Speaking to Nation.Africa, the chairman of the Taita Taveta County Assembly's Health Committee, Omar Ahmed, said drugs are available at health centres and they will investigate claims that patients were referred to private pharmacies.
"There are cases where I had to intervene for patients to get medicine at Moi County Referral Hospital, yet they had been told to buy at private chemists," he said.
Mr Omar said some workers may be trying to sabotage the county’s efforts to seal loopholes that aid the theft of drugs.