Counties in the Lake Region Economic Bloc (LREB) now want the national government to allow them to procure Covid-19 rapid test kits and import vaccines directly to address rising infections.
They also want the national government to help them with infrastructure to manufacture oxygen, which is needed in Covid-19 treatment.
Rapid testing is more cost-effective in improving case detection, they argue.
They want more focus put on the border and hotspot counties of Busia, Migori, Kisumu, Siaya, Kericho and Kisii.
LREB chairman and Kakamega Governor Wycliffe Oparanya said bureaucracy in the national government is delaying the procurement and delivery of essential items and drugs.
The three million jabs procured by the Ministry of Health, they said, are not enough to accelerate vaccination across the country.
"We are only calling upon our development partners to support the LREB response strategy by increasing the rapid testing kits by one million and [provide] 500,000 test kits for residents in the region," he said.
Mr Oparanya, with the bloc's vice-chairman, Kisii Governor James Ongwae, and their Kisumu counterpart Anyang' Nyong'o, spoke at a press briefing in Kisumu on Tuesday.
They issued a status update on infections and containment measures in the lake region counties.
The 13 counties - Kisumu, Siaya, Migori, Homa Bay, Kisii, Nyamira, Busia, Vihiga, Kakamega, Bungoma, Trans Nzoia, Bomet and Kericho - are under a partial lockdown.
They have reported 2,171 positive cases in the past one week while 5,189 were reported the previous week.
The highest number of positive cases in this period was from Kisumu, which recorded 451, followed by Siaya (446), Busia (263) and Homa Bay (220).
The total cases in the region as of June 20 were 28,866, accounting for 16.1 per cent of the total confirmed cases nationally.
Mr Oparanya also indicated that the counties need to import more oxygen-production equipment.
Kisii, Kakamega and Kisumu have oxygen plants but can only produce 300 litres per minute, while patients need 50 litres per minute.
Mr Ongwae said the national government should also step in to help counties to produce oxygen.
The Kisii County boss said the counties lacked the capacity to test Kenyans for Covid-19 and, therefore, rapid tests should be allowed as the first step in containing the virus.
"We are worried because protocols for rapid tests have not been given by the national government. It is all shrouded in mystery," he said.
"This is not about us looking at the government but looking at individuals. Do not wait for the government to help you do the things that can help stem the spread of the pandemic."
Governor Nyong'o said counties can find money to procure rapid test kits.
"We can set aside resources to buy rapid test kits, and even get them from Korea, where one can cost five dollars. The national government should allow us to do this because we will use stratified testing," he said.
"On vaccination, we should be allowed to import vaccines directly from development partners."
Kakamega and Kisumu plan to buy oxygen-generating equipment. The Kakamega one is expected to produce 1,000 litres per minute.
Prof Khama Rogo, the chairman of the LREB Committee of Eminent Persons, warned the public against flouting Covid-19 directives issued by the Ministry of Health to prevent the spread of the virus.
He advised residents of LREB counties not to wait to be treated or given oxygen, adding that by the time one requires it, it may be too late.
He also cited shortages of health personnel to handle the situation.
"Health workers are stretched, tired and are getting sick. Let us not ignore prevention. This is putting an unnecessary burden on them. Behaviour change is achievable," he said.