A fifth of Scotland's care home staff have been tested for coronavirus since the Scottish government promised to offer them all routine testing.
The health secretary announced on 28 May that all 50,000 care home workers would be offered weekly tests.
First Minister Nicola Sturgeon confirmed on Wednesday that about 11,000 staff had been tested.
She also said that 15,000 of the country's 35,000 care home residents had been given a test.
Scottish Conservative leader Jackson Carlaw said the figures showed that "tens of thousands are still going into work with vulnerable people with no idea whether or not they're carrying the disease".
He said it was "pathetic" that so few tests had been carried out, and called on Ms Sturgeon to "get a grip" of the situation.
Speaking at first minister's questions, Ms Sturgeon pointed to the falling number of deaths in Scotland's care homes as evidence that the government's actions were working.
She added: "The health secretary and I have been very clear that we want to see health boards accelerate progress. That is why were are publishing data health board by health board.
"It will allow us to track that progress, and indeed the public to scrutinise that progress."
However, Ms Sturgeon said it was important that the testing programme was "sound and sustainable".
She said: "I want to make sure that it is happening in a way that we can sustain over a period of time because this is testing that will happen regularly.
"It is not, as is happening in other parts of the UK, one-off testing.
"So it is right that health boards make sure that they carry it out quickly, but also carry out sustainably."
Mr Carlaw called on Ms Sturgeon to set a firm deadline for all care home workers to be tested.
The first minister said she would consider doing this - but went on to accuse Mr Carlaw of continually "politicking" by making "unsubstantiated claims" about the government's handling of the crisis.
The latest figures from the National Records of Scotland show that there have been 1,861 coronavirus-related deaths in care homes since the outbreak began.
This is marginally higher than the 1,854 deaths that have been recorded in hospitals.