Taoiseach Enda Kenny has said the Nice terror attack was an assault on innocent people during an occasion of joy and celebration.
Irish consular staff in Dublin and Paris were manning phone lines for concerned citizens and relatives.
Mr Kenny expressed deepest sympathies and solidarity with French President Francois Hollande and all of France.
"French people have suffered appallingly and have again been the victim of cynical and wanton violence," the Taoiseach said.
"We cannot and will not yield to this malevolence."
Consular staff are monitoring the situation closely, the Government said, and staff are seeking to establish if any victims were Irish.
Foreign Affairs Minister Charlie Flanagan urged Irish tourists in Nice to exercise caution and follow instructions from local authorities.
"I deplore the loss of life, and offer heartfelt condolences to the people of France from the people of Ireland," he said.
"This attack on people as they celebrated Bastille Day with friends and family on a fine summer's evening is particularly horrendous, and my thoughts and sympathies are with the relatives of the dead and injured."
Irish citizens in Nice who need embassy assistance were advised to call 0033 1441 76700.
Concerned relatives in Ireland were asked to contact the Department of Foreign Affairs in Dublin on 00353 1 4082000.
Ireland's ambassador to France Geraldine Byrne Nason said consular staff took a relatively low number of calls overnight in Paris and Dublin.
The situation is being monitored on an early basis, she said, but French authorities have not released details of those caught up in the attacks.
"In such a barbaric and unforeseen attack the information will be slow to come in terms of hard intelligence about those involved in the incident," she told RTE Radio.
Ms Byrne Nason said it is hard to find superlatives now to describe how vulnerable people are.
"Really I think we move beyond anything that we can reasonably articulate as behaviour we can understand. It is utterly barbaric," she said.
Catholic Primate of All Ireland Archbishop Eamon Martin asked for prayers for those killed and injured.
"The horrific scenes on the streets of Nice once more send shock waves into our homes and hearts. How helpless we all are when someone decides to deliberately and indiscriminately target human life," he said.
Micheal Martin, leader of the Fianna Fail party, called for solidarity with the people of France.
"My thoughts and prayers are with the families and friends of the people who were killed last night in Nice. It was a horrendous and callous attack on people's freedom as they celebrated Bastille Day," he said.
President Michael D Higgins spoke to French ambassador to Ireland Jean-Pierre Thebault and asked for messages of sympathy to be passed to President Hollande and the people of France.
"With its appalling loss of life, including children, it will be received with revulsion by all those who value democracy," Mr Higgins said.
"This cowardly attack in a public place on a national day of celebration must be condemned in the strongest terms. We must strengthen our resolve not to let such cold-blooded attacks undermine the way of life in our global community seeking to live in diversity and peace."
