Sinn Féin leader Mary Lou McDonald has said gardaí have been alerted to threats made against her.
Speaking at the first in a series of public rallies the party is organising around the country, Ms McDonald said she had received threats similar to those made against other party members but declined to provide any further detail.
She has also hit back at "ridiculous" claims by Taoiseach Leo Varadkar that the party's public rallies are a campaign of "intimidation and bullying".
The party has organised a number of public meetings across the country to build support in its bid to be part of the next government.
Full house in Corcaigh tonight for Sinn Féin's public meeting on a Government for Change 🇮🇪 pic.twitter.com/ufOOi3fSEy— Oisín McCann 🇵🇸 (@OisMacC) February 24, 2020
Speaking to well over 800 people at the first meeting at the Rochestown Park Hotel in Cork tonight, Ms McDonald said the comments were "ridiculous" and "over the top" from a "political establishment struggling with the result of the election".
She said: "I think they are having difficulties coming to terms with it but that is what they must do.
Ms McDonald said the meetings were "conversations with the people" and said it was not wise "that the election happens, people cast their vote and politicians disappear behind high walls and have discussions and leave people out".
"Why should [the conversation] it stop at election day? Where is it written down that you stop talking to people and you stop having a conversation with the community just because the election has come and gone?
"I actually think that that kind of politics and that type of attitude that the Taoiseach has played is the very thing that builds cynicism in politics," she said.
Sinn Féin finance spokesperson Pearse Doherty told the packed conference room that 4,000 people across the country were currently in the process of joining the party, while one attendee said he was "a traditional Fine Gael voter" but had "joined Sinn Féin last Wednesday".
Irish Solidarity-People Before Profit's Mick Barry was also in attendance.
He said people had "a right to free speech and the right to hold public meetings" and that the intimidation was coming from "the political establishment".