Micheal Martin issued a "note of warning" over the Indian Covid-19 variant as he said he is keeping a "very close eye" on rising hospital and case numbers in the UK.
The mutation is spreading across the Irish Sea and the Taoiseach said that despite the improving situation here, certain parts of England are seeing a rise in infections.
The Taoiseach also set a new vaccine target as he aims for 70% of the adult population to be fully vaccinated by the end of next month.
He told Newstalk Breakfast: "Well can I just put one note of warning and concern is the Indian variant and what is happening in the United Kingdom, we said we would keep a close eye on that and we are keeping a close eye on that."
He added: "We're making good progress, the hospitalisations this morning are 77 in hospital, 27 in ICU, so it's so far, so good. Although there is a Bank Holiday effect in terms of the numbers which will see numbers increase towards the end of the week.
"But we are just watching the British situation and the fact they are looking at higher hospitalisations, and in particular geographies in Britain the numbers are going up, so we're keeping a very close eye on that."
And Mr Martin confirmed that the government's latest vaccine target is to see 70% of the adult population fully vaccinated by the end of July.
He continued: "I think we're in a good position, I think the target we are aiming for by the end of July, dependent on supply, is that we have 70% fully vaccinated.
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"The decision from NIAC was to bring forward the AstraZeneca interval dosage period to eight weeks, the HSE are working on that progressively which will help us on the fully vaccinated side of the situation, which is where Europe wants to be by the end of July.
"We don't have an exact timeline [on when everyone will be vaccinated], but I think June is going to be a very good month, the last two weeks of June are looking very good in terms of supply from Pfzier-BioNTech in particular.
"The AstraZeneca visibility is also improving. I met with AstraZeneca last week on that issue and they have developed new capacities in Spain and Germany, and therefore they are looking better than perhaps they did earlier in the pandemic in terms of supply."
