Taoiseach Enda Kenny expressed his deep shock at the "appalling" murder of Jo Cox in broad daylight.
The Fine Gael leader yesterday suspended his campaign to encourage the estimated 60,000 Irish people living in the UK to vote in the referendum on Britain's future in Europe following the news of Ms Cox's death.
"I think it's an appalling crime that a public representative going about her public duty could be shot down in the street and loses her life and has her value to the community and to her family taken away," Mr Kenny said at a event hosted by the Greater Manchester chamber of commerce.
At a further event this morning, Mr Kenny will also avoid making any comment on next week's 'Brexit' referendum.
Meanwhile, Tanaiste and Minister for Justice Frances Fitzgerald said she was "deeply shocked" by the death of Ms Cox and described it as "an attack on democracy and on democratic freedoms which I utterly condemn".
"This is truly a disturbing and horrific act," she said. My thoughts are with her family and friends. We also stand in solidarity with our colleagues in Westminster who have suffered this great loss.
President Michael D Higgins said he learned of the MP's death with "great sadness".
"As all of us sympathise with her family, including her young children, all of us who are committed to democratic politics must also acknowledge our being shocked, appalled and outraged at the attack on her.
"To see a young parliamentarian killed in the course of her work is especially shocking. Her loss must not be in vain." he added.