A call has been made to the Minister for Justice, Mr McDowell to make inquiries about why the celebrations for the Irish soccer squad could not take place in Dublin's city centre rather than the Phoenix Park.
Mr Ruairí Quinn, the Labour leader, said it was "sad that the gardaí feel incapable of being able to provide the necessary security to ensure people's safety".
Mr Quinn also said they deserved "formal recognition", a suggestion Ms Harney said the Taoiseach would consider.
The decision to host the celebration in the Phoenix Park had been made for security reasons. That decision reflected "none too well on our collective efforts to provide security on what is a happy and joyful occasion".
Mr Quinn asked the Minister for Justice to find out why "this celebration cannot be done safely, properly and joyfully on our streets as well". He asked "if it was safe for the former President Bill Clinton to address the people of Dublin from College Green and not pose a security risk, surely it would have been equally as safe for Mick McCarthy and the lads to come through the streets of Dublin".
He raised the issue during statements on Ireland's World Cup performance. The Taoiseach, praised the team, the FAI and Mick McCarthy and thanked them "individually and collectively for the enormous satisfaction and pride that they gave to the country". The Fine Gael leader, Mr Enda Kenny, said they and the supporters "brought a sense of excitement, passion and courage to their games in the World Cup".
The Green party leader, Mr Trevor Sargent, said safety fears might have been expressed in the 1990 celebrations, but "there has been a dozen years in the meantime to put those safety fears to the test and come up with solutions".