NHS Highland has stepped in to play a greater role in the facility after concerns were raised.
Education secretary John Swinney says he is 'wrestling' with the issues amid plans for a phased return to schools in August.
There have been more than 3600 confirmed or suspected coronavirus deaths in Scotland, weekly figures show.
HC-One will keep providing services at the Home Farm Care Home in Portree until at least June 10.
Coronavirus testing in Scotland has also been extended to anyone over the age of five with symptoms.
Speaking at First Minister's Questions, Richard Leonard said his uncle had died in a care home with the virus.
It follows weekly figures which show a third of deaths involving Covid-19 occurred in care homes.
The Care Inspectorate said it was aware of the deaths at Kingswells Care Home in Aberdeen.