Michael D Higgins also met the British ambassador to Ireland
President Michael D Higgins and Taoiseach Enda Kenny have signed a book of condolence at the British embassy in Dublin for vicitims of the Westminster terror attack.
President Higgins also met the British ambassador, Robin Barnett, and said it was very important to say the criminal act that this was.
The president said he would be writing to Queen Elizabeth II.
It comes as the death toll from the attack was raised to five, after a 75-year-old man who was seriously injured died in hospital after his life support was turned off.
The man, named as Leslie Rhodes, died at King's College Hospital in the city.
Two people remain in hospital in critical condition - one with life threatening injuries.
The book of condolence is open to the public on the 24th and 27th of March from 10.00am to 4.00pm at the British embassy on Merrion Road in Dublin.
A book of condolence will be open on 24 & 27 March, 10-4pm at the British Embassy, Merrion Rd, for the victims of the #Westminster attack— British Embassy (@BritEmbDublin) March 23, 2017
Those dead include attacker Khalid Masood - whose birth name was Adrian Russell Ajao, according to the Metropolitan Police.
They say Masood had also previously gone by the name Adrian Elms, and possibly a "number of other names".
British police made two further arrests overnight in the West Midlands and North West areas. In total, nine people remain in custody.
While he was born in Kent on Christmas Day 1964, detectives believe he had been living most recently in the West Midlands.
In a statement, the Metropolitan Police said there was "no prior intelligence about his intent to mount a terrorist attack".
Masood "was not the subject of any current investigations", they said.
Nevertheless, "he was known to police and has a range of previous convictions for assaults, including GBH, possession of offensive weapons and public order offences".
The statement added: "His first conviction was in November 1983 for criminal damage and his last conviction was in December 2003 for possession of a knife.
"He has not been convicted for any terrorism offences.
Although some of those Masood was involved with included people suspected of being keen to travel to join jihadi groups overseas, Masood "himself never did so," said a US government source, who spoke to Reuters news agency on condition of anonymity.
British Prime Minister Theresa May said Masood was a "peripheral" figure who had once been investigated by MI5 over concerns about violent extremism.
A former neighbour from Birmingham told Reuters: "When I saw the pictures on TV and in the papers of the man who carried out the attack, I recognized him as the man who used to live next door.
""He had a young child, who I'd think was about 5 or 6 years old. There was a woman living there with him," she added.
According to The Sun, on the night before the attack Masood stayed at a budget hotel in Brighton and 'ate a takeaway kebab'.
On Thursday evening people came together in London's Trafalgar Square for a candlelit vigil to show defiance and solidarity.
London Mayor Sadiq Khan told the packed square: "Those evil and twisted individuals who tried to destroy our shared way of life will never succeed and we condemn them.
"When Londoners face adversity we always pull together. We stand up for our values and show the world we are the greatest city in the world."
A young woman said: "We all have to stick together and show support and solidarity. They might have scared us but they won't beat us."
A man who said he was from the Muslim community added: "This is our home. You've got to stand together.
"When you get such a person as this - I cannot even express what sort of brain he had. This is time to show we are together.
"Love for all; hatred for none - that is our message. The word Islam means peace. Going out and doing this sort of atrocity is...(the) opposite of Islam."
British teacher Aysha Frade and US tourist Kurt Cochran were the other civilians killed when Masood drove his Hyundai into pedestrians on Westminster Bridge.
Unarmed policeman PC Keith Palmer (48) was then stabbed to death by the 52-year-old terrorist in the grounds of the British parliament.
Dozens of other people were injured - including an Irish citizen - as well as nationals of Britain, France, Romania, South Korea, Greece, Germany, Poland, China, Italy and the US.
Kent-born Masood, who was shot dead by police 20 metres inside the gates of the parliament, used a number of aliases and was investigated by MI5 some years ago over concerns of violent extremism.
British Home Secretary Amber Rudd denied there had been an intelligence failure.
Mrs Rudd said "one did get through" on Wednesday but she had "complete confidence in our intelligence services".
"My experience of the intelligence services is they do a remarkably good job," she said.
"Let's remember this is the first Islamist terrorist attack for four years. They've foiled 13 since 2013.
"I'm sure we'll get more information in the next few days and weeks."
A review of security is taking place at the British parliament.