The Taoiseach has been called on to seek additional vaccines from the US when he speaks to President Joe Biden next week.
Micheál Martin is to hold a virtual meeting with the president next week to mark the annual St Patrick's Day celebrations.
It comes as news emerged that the US is sitting on upwards of 50 million doses of the AstraZeneca vaccine, which cannot be used there as they are still awaiting the results of clinical trials.
Fianna Fáil MEP Billy Kelleher has written to both the Taoiseach and President Biden urging them to consider the issue.
He said: "These vaccines all have a limited shelf life, and with the FDA having not authorised AstraZeneca's use in the US, they need to be used somewhere and soon.
"This is an opportunity that cannot be missed or ignored. It's too important not to at least try.
"Just one million doses would be transformative for the vaccine programme in Ireland, and it needs to be on the agenda next week."
The New York Times reported on Friday that 30 million vaccine doses are currently bottled at AstraZeneca's facility in West Chester, Ohio.
Tens of millions more are ready to be bottled into vials at a factory in Baltimore, Maryland.
However, the paper reports that the White House has not yet decided what to do with the doses, with officials split on whether to send them abroad or keep them in the US.
Writing to President Biden, Mr Kelleher said: "There is a global need to vaccinate people everywhere as quickly as possible.
"While I respect your right to protect the wellbeing of your citizens above others, I believe the United States, with its massive industrial capacity, can afford to share a proportion of these stockpiled vaccines with other countries such as Ireland.
"I would urge you to consider any request from An Taoiseach, or indeed the European Union, to relax the export bans currently in operation in the United States and allow us to make use of these precious vaccines."
Writing to the Taoiseach, Mr Kelleher said there may be "upwards of 50 million doses in refrigeration" throughout the US.
He added: "Ireland's special and deep relationship with the United States and President Biden's love of our country and his own Irish-American heritage lends itself well to a successful agreement being concluded.
"Ireland must use its position as the natural cultural and diplomatic bridge between the United States and the EU for the benefit of all.
"Taoiseach, I have no doubt that this is already on your agenda, and I know that you and the Government are actively seeking new ways of increasing Ireland's supply of Covid-19 vaccines.
"No one can or should ever fault Ireland's Taoiseach from doing whatever he or she can to protect the lives of our citizens."