The Sinn Féin leader has claimed people have had to travel up to four hours to get a COVID-19 PCR test.
Mary Lou McDonald says more capacity must be provided immediately.
Opposition parties have been voicing their concerns over the struggles many people are having when trying to book a PCR test.
As of lunchtime today, only Letterkenny testing centre had slots available today, while just four centres nationally have availability for tomorrow.
The HSE has said it's trying to provide more tests but will be prioritising them based on clinical need.
In the Dáil, Deputy McDonald said: "For people experiencing symptoms or in a household where someone is experiencing symptoms, not being able to access these tests is frustrating and frightening for people.
"Indeed, many have had to travel up to four hours for a test - that's not acceptable."
Taoiseach Micheál Martin has said there's been a "very significant expansion of PCR testing", with 210,000 tests carried out in the last week.
He said the HSE is doing everything it possibly can to expand testing further, with testing currently at a level "we never thought we would need".
Deputy chief medical officer Dr Ronan Glynn today said no health service in the world would be able to meet the current demand for tests.
He says as many as 700,000 people have had flu, cold or COVID-like symptoms in the past week - and the system, which has the capacity for around 200,000 tests a week, has to prioritise.
However, he said he understands it's frustrating when people are unable to book a test in a timely manner.