Kindiki said he had advised Koome to write the letter.
"I advised that whenever there are operational issues, they can brief us so we can respond to them," the CS said.
But MPs faulted the move, arguing that it undermined the Constitution. Despite Kindiki's assurances that there were no differences between Koome and Kinuthia, lawmakers insisted that Koome should appear before them.
"We are not summoning the IG to harass him but to question him, as the people's representatives, about the roadside declarations he has been making," said Nambale MP Geoffrey Mulanya.
Wa Muchomba lamented that the IG and his two deputies, as well as the uniformed members of the NPSC, have previously snubbed her committee's sittings, attended only by ununiformed members.
"The IG must come here to tell us if the issues were sorted," she said, raising concern over a major rift within the commission.
"The NPSC chairman told us that every time they hold meetings, they are denied quorum by their uniformed colleagues," she said, urging Kindiki to sort out the mess within the NPSC.
Kindiki said he had held discussions with the two, who in June, feuded over whose role it was to promote police officers.
The Interior CS, who once again called out the pair over their spat, said both the IG and the NPSC had a role in promotions. Koome's role, Kindiki said, was to recommend promotions, with the NPSC giving the promotions legal backing.
"We cannot have someone commanding an armed organisation and say that he has no say in the promotion of his officers," he stated, warning that Koome and Kinuthia had risked removal for their conduct.