Mr Coveney, speaking in Brussels ahead of a Council of Ministers meeting, confirmed there will be cuts to current and capital expenditure.
The IFA said massively disproportionate cuts have already been meted out to the farming sector.
The clash occurred as thousands of farmers headed to Ratheniska, Co Laois, for the National Ploughing Championships which Mr Coveney is due to visit tomorrow.
Mr Coveney said agriculture had to take its “fair share” of reductions.
Responding to the IFA claims of disproportionate cuts compared to other Government departments, he said it depended on how expenditure was calculated.
“If you include the money that is spent on agriculture that comes from an EU budget then that’s not the case. If you only count the exchequer’s contribution towards the agriculture budget, then yes, the cuts have been significant.”
He said there was recognition that the agri-food sector’s momentum needed to be maintained.
IFA president John Bryan said it was not acceptable for the minister to use EU funding to try and mask the massively disproportionate Government cuts that have been meted out to the farming sector in recent budgets.
He said the proportionate exchequer spend on agriculture since 2004 has fallen by 25% (from 3.04% in 2004 of the total national budget to 2.26% in 2013).
“Since 2008, the agriculture budget has been reduced by a greater percentage than any other major government department, with total funding cut by 41.2%, compared to an average reduction across all government departments of 12.6%.”
Mr Bryan said total expenditure on farm schemes between 2011 and 2013 fell by 18% or €119m.
This compares to a reduction in expenditure of 8%, or €60m across all other budgetary headings within the agriculture budget.
Mr Bryan said his message for the minister and politicians visiting the IFA stand at the ploughing championships this week would be that investment in primary production supports jobs and exports and provides a sustainable stimulus for the local and wider economy.