The British government has said it does not currently have a surplus of Covid-19 vaccines, but "will consider how these are allocated as they become available."
A government spokesman said its first priority is to protect the British public and it remains on course "to offer a first dose to all over 50s in the UK by April 15th and all UK adults by the end of July".
Health minister Matt Hancock said that a total of 30,151,287 people have received the first dose of a Covid-19 vaccine, representing around 57% of all adults.
A total of 3,527,481 people have been given their second doses.
"The vaccine is saving lives and is our route out of this pandemic," he said.
Earlier, Northern Ireland First Minister Arlene Foster said she believes the British government should share vaccine stocks with Ireland once its vaccination programme is completed.
Ms Foster said she recommended the proposal to Prime Minister Boris Johnson when he visited Enniskillen earlier this month, and will be making the point again the next time she speaks to him.
Speaking on RTÉ's This Week, Ms Foster said she thought that the idea "is a runner".
She said: "I think it's important that we continue the conversation and I'll be listening very carefully to what our medical advisers are saying about the roll-out of the vaccine in Northern Ireland, where it is in the Republic of Ireland and what that means for both jurisdictions."
The DUP leader added: "I think it's the right thing that should happen, I think it's a very practical thing to do and I think it should happen and hopefully it will."
When asked if she had discussed the idea with Taoiseach Micheál Martin she said she had not spoken with him "for quite some time now".
Ms Foster also said Europe was too slow in how it procured the vaccine.
Minister for Foreign Affairs Simon Coveney said no offer of excess vaccines has been made to the Government from the UK government.
Speaking on RTÉ's This Week, he said that "if there was, we would be very interested in talking to the British government about that".
He said that there are tens of millions of vaccines that have yet to be distributed in the UK and there are tens of millions of people there yet to get the vaccine and while there may be excess vaccines, he said he does not think "we are realistically looking at that for many, many weeks yet".
He said that it is "welcome language" to hear Ms Foster suggesting that any excess vaccine capacity could be shared with Ireland.
Yesterday, the 50-year-old DUP leader received her first shot of the AstraZeneca vaccine in Co Fermanagh.
As of Friday, 825,310 vaccines had been administered in Northern Ireland - 711,673 of which were first doses and 113,637 were second doses.
The North is on course to offer first jabs to the entire adult population - 1.4 million - by July and on Monday a new mass vaccination centre will begin operations in Belfast's SSE Arena.
As of 24 March, 732,678 doses of Covid-19 vaccine have been administered in the Republic, with 529,984 people receiving their first dose and 202,694 receiving their second.
A Government spokesperson said this morning that the Irish and UK governments "maintain close contact across all matters of common interest", but is not aware of a specific UK plan to share vaccines with Ireland.
The spokesperson said: "The UK has previously indicated that once it has achieved a high level of vaccination of its own population, it would consider sharing vaccines with other countries.
"We are not aware of any specific plans to share vaccines with Ireland at this stage.
"The Irish and UK governments maintain close contact across all matters of common interest."
However, speaking on Sky News this morning, the UK's Culture Secretary Oliver Dowden said Britain does not "currently have a surplus" of coronavirus vaccines.
"Clearly, our first priority is ensuring we deliver vaccines in the United Kingdom. We clearly don't currently have a surplus of vaccines, should we get to the point where we have a surplus of vaccines we'd make decisions on the allocation of that surplus," he said.
More than 25 million people in England have been vaccinated with their first dose, with the number of people receiving their second dose reaching a new weekly high.
Additional reporting PA