Fine Gael leader Leo Varadkar is to establish special Cabinet subcommittee on national security when he takes over as taoiseach, which is expected to happen in a week and a half.
Mr Varadkar’s proposal will be along the same lines as the Cobra committee in Britain, which is convened and chaired by the prime minister to deal with terrorist attacks and other incidents.
This will be done within the first 50 days of his government.
"Although Ireland is not at high risk of a terrorist attack, it is important to be prepared for every eventuality," a spokesman for Mr Varadkar said. "The new committee will allow greater ministerial involvement in preparing for and managing major security threats, and more extensive cross-departmental cooperation on these issues."
In the past, the Government convenes meetings of the National Emergency Coordination Committee to deal with, for example, extreme weather incidents such as flooding.
Mr Varadkar’s spokesman said the existing structures are largely driven by officials and are geared towards natural disasters, whereas the new Cabinet subcommittee would allow for greater political involvement.
Meanwhile President Michael D Higgins has extended his sympathies and those of the Irish people to the victims and their families.
“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,” Mr Higgins said.
"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."
Tánaiste and Minister for Justice Frances Fitzgerald said the attack in London was "another depraved and cowardly attack on innocent people".
“Our first thoughts are with the families of those killed and with the injured victims,” she said.
Ms Fitzgerald said she had been briefed on developments on Sunday morning by Garda Commissioner Nóirín O’Sullivan.
“The Garda authorities remain in close contact with their counterparts in London and will offer whatever support they can,” she said.
Minister for Foreign Affairs Charlie Flanagan said Ireland stood with Britain following Saturday night's events.
“For the second time in two weeks, the ordinary people of the UK have been subjected to cowardly and barbaric attacks. Ireland stands with the UK and condemns these acts utterly,” Mr Flanagan said.
The authorities here continued to closely monitor the situation, he added.
Fianna Fáil leader Micheál Martin also expressed his sympathies to the families and friends of those who died or who were injured.
“This was a callous attack on people who were simply enjoying life,” he said.
“Fianna Fáil stands with the people of London. London has withstood attacks of this nature before, and it became stronger as a result. Last night’s attack will, I have no doubt, bring Londoners of all creeds, races, and ethnicities, even more together and will make the city even stronger.”
Sinn Féin president Gerry Adams said he absolutely condemned Saturday's "horrendous attacks" .
“On behalf of Sinn Féin, I offer my sincere condolences to the victims and the families of those killed and injured and to the people of London,” Mr Adams said.
In the North, PSNI Chief Constable George Hamilton said his thoughts and sympathies were with the people of London following the "horrendous" attack. "We also send our support to our colleagues in the Metropolitan Police, City of London Police, British Transport Police and all the emergency services that responded last night," he said.
Anyone who has serious concerns about loved ones in London may contact the Department of Foreign Affairs in Dublin on 01-4082000, or the Irish Embassy in London on 00-44-20-72352171.