President Michael D Higgins and Taoiseach Enda Kenny have signed a book of condolence at the British embassy in Dublin for the victims of this week's terror attack in London.
The President expressed his solidarity to the British ambassador, Dominick Chilcott, saying it is very important to see the atrocity as a criminal act.
Mr Higgins also said he would be writing to Queen Elizabeth II.
The British ambassador expressed his thanks to the Irish president for his attendance.
"We 're deeply honoured that the president has come here to express solidarity on behalf of the Irish people. I have to say since the news of the terrible incident first broke we have been inundated with people expressing support and sympathy.
"We are deeply grateful to the president for joining us in this formal way but as I say we are very well aware that the people of Ireland have joined with the people of the United Kingdom reflecting the very special and unique bond that exists between our two countries.
Police Officer PC Keith Palmer (48), retired window cleaner Leslie Rhodes (75), mum Aysha Frade and US tourist Kurt Cochran (54) all lost their lives in the attack.
Earlier, two more "significant arrests" have been made in connection with the Westminster attack, police have said.
Scotland Yard's top anti-terror officer Mark Rowley said the suspects were held overnight in the West Midlands and north west as he revealed that the killer's birth name was Adrian Russell Ajao.
Mr Rowley appealed to the public for information about the killer, who was also known as Adrian Elms but was using the name Khalid Masood at the time of the attack.
The officer also revealed that the fourth member of the public injured in the attack, who died in hospital last night, was 75-year-old Leslie Rhodes from Streatham, south London.
Mr Rowley said two people remain in hospital in a critical condition, one with a life-threatening injuries. Two police officers injured in the attack are also in hospital with "significant injuries".
Mr Rowley said: "We remain keen to hear from anyone who knew Khalid Masood well, understands who his associates were and can provide us with information about places he has recently visited.
"There might be people out there who did have concerns about Masood but did not feel comfortable for whatever reason in passing those concerns to us."
Additional reporting by Press Association