And Sinn Fein MEP Matt Carthy has urged enterprise minister Mary Mitchell O'Connor to delay it. The Commission this month went against its own legal advice by sending it back to parliaments for final sign-off, and says it intends to sign and start the deal in October at the EU-Canada summit.
Mr Carthy said Ms O'Connor was "reckless" for supporting early application before the parliamentary votes have had time to go through.
"Almost all of the dangers that have been highlighted in the TTIP US trade deal are also contained within CETA," Mr Carthy said.
However, EU companies have recently appealed to Donald Tusk, who chairs regular EU summits, to make sure the agreement takes effect as soon as possible. BusinessEurope, a group representing EU companies, said the swift signature of the agreement was a "important signal in a time of so many challenges and uncertainties".
"If the provisional application of CETA is delayed, the signal sent to European companies and other trading partners would be that the EU is no longer able to deliver on one of its key policy areas, one that is critical for boosting economic growth and job creation," the group said in a letter to Mr Tusk last week.
Despite the controversies, the EU is pressing ahead other trade talks, launching negotiations last week with Indonesia.
Climate targets will pose big challenge for agri sector
Last week saw the EU hand out national 2030 emission reduction targets for certain sectors, including agriculture.
The climate targets will be a challenge, as they call for major investments to clean up Ireland's largest-emitting sector.
Agriculture is Ireland's largest indigenous industry, generating 10.7pc of all goods exports and accounting for 8.4pc of total employment, according to government figures.
But it also accounts for 30pc of Ireland's total carbon emissions, and emissions in the sector are rising, according to the Environmental Protection Agency.
A recent study by NGO coalitions Stop Climate Chaos and the Environmental Pillar found that Irish agriculture emits more per calorie of bovine food produced than the European average.
Minister for Agriculture Michael Creed has said Ireland's approach is one of "carbon neutrality in the agriculture and land-use sector, including forestry".
The EU's national emission reduction targets range from zero to 40pc for agriculture, transport, buildings and waste (compared to 2005 levels).
The targets allow nine small, agriculture-heavy or forest-rich countries - including Ireland - to use carbon sinks, such as forests and grasslands, to help meet the targets, and allow all countries some flexibility to transfer excess credits from the emissions trading scheme (ETS).
Ireland got a 30pc target but is entitled to the highest leeway on forests and ETS allowances.