Taoiseach Micheál Martin has been told by Boris Johnson that the UK is not in a position to give surplus Covid-19 vaccines to Ireland.
Mr Martin said the British prime minister's first priority is to vaccinate people living in the UK.
Ireland is struggling to meet its vaccine targets following a number of delivery issues.
These are affecting the Government's vaccine programme, with question marks over its plan to roll out one million vaccines in April.
Mr Martin said he was "disappointed" with some of the issues relating to the vaccine supply.
Speaking on Tuesday, Mr Martin said: "The British Prime Minister has made it clear to me that obviously his first priority is to vaccinate his people.
"It would be helpful to Ireland if the situation arose, but right now he has to concentrate on vaccinating his own people.
"Until then, he won't be in a position to give vaccines to anybody and he has made that point to me, which I thought was fairly obvious at the outset."
Asked about the supply, Mr Martin said: "We are disappointed with quarter one in terms of the issues, but in terms of protecting the most vulnerable, we have made progress on that and the impact of the vaccines is very positive.
"We have seen that in terms of healthcare workers, hospitals and in nursing homes in particular, and now out in the community in the over-80s. That is good news.
"We have very good vaccines that are giving protection to people as well."
Ireland has extended its lockdown restrictions until April 5 and Mr Martin said the Government will review the Level 5 restrictions in a number of weeks.
He added: "We will take the advice from Nphet (National Public Health Emergency Team) and public health, and concentrate on the areas already identified in terms of the sporting and outdoor activity that we indicated we would look at. It will depend on where the numbers are.
"We are making progress as a country and the adherence to the regulations does matter, particularly in context of a variant.
"We are taking the pressure off the frontline workers. We will be in a better position before April 5 to make informed decisions."
A further 30 Covid-19 linked deaths were reported in Ireland on Tuesday. Nphet also confirmed another 311 positive cases.
As of 8am on Tuesday, 397 Covid-19 patients were in hospital, of whom 95 were in intensive care units.