An e-voting lobby group has claimed the Minister for the Environment, Mr Cullen, has refused requests for a meeting to address their concerns over the introduction of the new system.
The Irish Citizens for Trustworthy Voting (ICTE) also claim that, despite assurances to the contrary, no "continued dialogue" has been conducted between them and the Department of the Environment.
"We realise that the Minister's schedule is very full, but this issue is of critical importance and should at the top of his list of priorities."
The ICTE is calling for the introduction of a paper audit trail with any e-voting system.
A spokesperson for the Minster for the Environment, Mr Cullen, said the Minister wanted to allow the Commission on Electronic Voting to complete its work before holding any further meetings on the issue.
Minister Cullen has previously met with the ICTE, among other groups, on issues concerning the introduction of e-voting, the spokesperson added.
The Commission on Electronic Voting and Counting has been set up to inquire into electronic voting and will have the power to recommend its postponement or abandonment when it produces its first report.
The members of the Electronic Voting and Counting Commission are High Court judge, Mr Justice Matthew P Smith, Mr Kieran Coughlan, clerk of the Dáil; Ms Deirdre Lane, clerk of the Seanad; Mr Danny O'Hare, the former head of Dublin City University; and Mr Brian Sweeney, chairman and former chief executive of Siemens Ireland.
The new e-voting system is set to be used nationwide for the first time in the European Elections on June 11th next.
A similar electronic ballot was used in a limited form in the 2002 Nice Treaty poll and that year's General Election.