Sinn Fein is facing a backlash over the party's decision to vote against anti-terrorism laws introduced in the wake of the militant Islamist extremist attack on Paris.
Gerry Adams' party refused to back a motion seeking to allow EU countries to share airline passenger records.
The EU Passenger Name Record (PNR) directive is part of a suite of measures aimed at clamping down on the growing threat from Islamic fundamentalists seeking to wage war on Europe.
It requires airlines to share information such as passport numbers, travel dates and baggage details that they gather from passengers to enable authorities to identify terror suspects.
However, Sinn Fein voted against a motion calling for the directive to be enacted by the end of the year when it went before the European Parliament three weeks ago.
The party voted against a similar motion earlier this year. Sinn Fein also voted against a motion condemning Isil and supporting international efforts against the terror group in March.
Fine Gael MEP Brian Hayes called on Sinn Fein to support the EU's response against the rise of the brutal Islamic terrorist organisation.
"I can't understand why Sinn Fein would oppose this sensible security directive," he told the Sunday Independent.
"After the Paris attacks we all need to realise our responsibility in countering terrorism."
Fine Gael's Dublin Rathdown candidate, Josepha Madigan, said there is "no excuse" for Sinn Fein's refusal to support the EU's response to terrorism.
"They have always had a laissez-faire attitude to law and order and security. It seems they cannot be trusted to act responsibly when it comes to security issues," said Ms Madigan.
"It's ironic and deeply worrying, given their past, that Sinn Fein refuses to support this directive which would enable authorities to identify the movements of those suspected of serious crime or terrorism."
Sinn Fein insisted that it did not support the passenger information-sharing directive because it believes the measures infringe on personal privacy rights "without just cause".
A spokesman said the party is "totally opposed to the attacks on the Kurds and others in the region being carried out by Isis" but does not believe that military intervention is the appropriate action to take to resolve the conflict.