All patients over 70 who are admitted to hospital for any reason will now be tested for Covid-19, First Minister Nicola Sturgeon has announced.
She told her daily briefing this would not just apply to those with symptoms of the coronavirus.
Ms Sturgeon said they would be tested on admission to hospital and every four days throughout their stay.
"That will help us identify if the virus is being transmitted in the hospital and how and where," she said.
The first minister told the briefing there had been "steady progress on increasing testing capacity" over the past month and the Scottish government would reach its target of being able to carry out 3,500 tests per day by the end of April.
Ms Sturgeon said that as a result of extra capacity testing, this had already been expanded to people in "priority" areas.
She said tests were currently made available and processed within NHS labs for:
- people in hospital with symptoms of Covid-19 and all those in intensive care
- people who have been referred for testing by their local Covid hubs
- people in care homes who have symptoms
- people who are being admitted to care homes
- and key workers in health and care services and where appropriate their family members. More than 20,000 people in that category have now been tested.
In addition, key workers in other sectors, for instance the prison service, are able to book tests online for the drive-through centres that have been established around the country, Ms Sturgeon said.
The first minister said NHS boards were now being asked to test everyone over 70 who was admitted to hospital for any reason.
She said: "Although we don't usually test people without symptoms because the test is not totally reliable in those cases, we do think that there could be a benefit in testing older people, both on their admission to hospital and at intervals thereafter."
Meanwhile, Health Secretary Jeane Freeman later told parliament that half of all adult care homes (538) in Scotland had notified the Care Inspectorate of at least one suspected case of Covid-19.
She said 384 (35%) of care homes had a current outbreak, where more than resident had exhibited symptoms during the past 14 days.
The latest figures show there have been 2,935 cumulative cases of suspected Covid-19 in care homes, up 204 on the previous day.