The Taoiseach Enda Kenny is among the world leaders expressing their shock at the attack in London.
Mr Kenny tweeted last night: "Terrible news coming from London - we stand with our close neighbours again tonight."
Terrible news coming from London - we stand with our close neighbours again tonight. @IrelandEmbGB monitoring the situation.— Enda Kenny (@EndaKennyTD) June 3, 2017
He released a statement this morning that said: "We utterly condemn the cowardly attack in London last night and reject the warped motives and world view behind them. This is sheer madness.
"Ireland will continue to work exceptionally closely with the UK and all of our colleagues on security matters and prevention as far as possible. Full details of this attack are only emerging. I have been in contact with the Tánaiste and Minister for Justice Frances Fitzgerald this morning and will speak to Prime Minister May when appropriate.
"The Irish people stand with our close neighbours once again.
"We continue to closely monitor the situation. Anyone who has serious concerns about loved ones in London can contact the Department of Foreign Affairs in Dublin on 01 408 2000, or the Irish Embassy in London on 00 44 207 235 2171."
The Tánaiste and Minister for Justice and Equality Frances Fitzgerald said: "Last night's attack in London is another depraved and cowardly attack on innocent people. Our first thoughts are with the families of those killed and with the injured victims.
"I have spoken this morning with the Garda Commissioner who briefed me on developments. The Garda Authorities remain in close contact with their counterparts in London and will offer whatever support they can".
Minister for Foreign affairs Charlie Flanagan issued a statement this morning to say: "For the second time in two weeks, the ordinary people of the UK have been subjected to cowardly and barbaric attacks," adding that his department is continuing to closely monitor the situation.
Responding to the horrific attack in London, President of Ireland Michael D. Higgins said: "This latest terrible attack in London will be rightly condemned by all those who believe in the rights of our public to live their lives in the public space.
"To our neighbours in the United Kingdom I send the sympathy and support of the Irish people, and in particular the heartfelt sympathy to the families of those who have lost their lives, and our thoughts and wishes for such recovery as is possible to the injured and their families."
Fine Gael Leader and Minister for Social Protection Leo Varadkar has expressed his shock at the latest attack on civilians in London.
"Once again innocent people have been targeted in the most craven and horrific manner. We extend our solidarity to the people of the UK and condemn this incident in the strongest possible terms.
"The fact that this comes so soon after the Manchester attack only adds to the horror.
"Irish authorities are in constant contact with their counterparts in the UK. If you have any fears regarding family or friends the Department of Foreign Affairs can be contacted on 01 408 2000 and the Irish Embassy in London is at 00 44 207 235 2171."
French President Emanuel Macron said France was "more than ever at Britain's side" after the attacks.
US President Donald Trump has offered his condolences, saying America is ready to help.
The city's mayor Sadiq Khan has described it as "deliberate and cowardly".